Help Do all the problems!!!

[SOWHAT0819]

7. Find the weekly yield (in %) for an investment that has a interest rate of 6.7% compounded quarterly

8. Find the accumulated amount of P3,001 for 5 years and 8 months at 5.9% simple interest.

9. Find the time (in years) for a P30,000 deposit to triple itself at 5% compounded monthly

14. Find the accumulated amount of P3,609 invested 0.07% compound daily at for a period of 12 years, Do not include units in your final answer. Round off to 4 decimal point.

17. Find the weekly yield (in %) for an investment that has a interest rate of 5.22% compounded quarterly.

18. Find the accumulated amount of P4,731 for 4 years and 8 months at 9.9% simple interest.

19. How much money should be invested in an account that earns 7.5% interest, compounded quarterly, in order to have P100,000 in 8 years?

23. If you can earn 11.8% on your investments yearly, and you would like to accumulate P251,453 for your savings at the end of 15 years, how much must you invest annually to reach your goal?

25. How much money should be invested in an account that earns 7.5% interest, compounded quarterly, in order to have P100,000 in 8 years26. Manny have the present worth of personnel salaries over the next 10 years. He has four employees whose combined salaries thru the end of this year are P 650,000. If he expects to give each employee a raise of 5% each year, the present worth of his employees' salaries at an interest rate of 12% per year.

28. Determine the final value if you invest P33,742 into a certificate of deposit that has an annual interest rate of 9.5% compounded quarterly for 4 years. (answer :49121.71, double check!!)

31. Find the accumulated amount of P4,928 invested 0.1% compound daily at for a period of 13 years (answer: 4992.4821 ,double check!!!)

32. Find the accumulated amount of P4,425 for 3 years and 8 months at 8.8% simple interest

34. Determine the final value if you invest P23,367 into a certificate of deposit that has an annual interest rate of 10.1% compounded quarterly for 5 years. ( answer: 38476.762, double check!!)

35. Find the accumulated amount of P4,734 invested 0.1% compound daily at for a period of 18 years.

Determine the capitalized cost at 7.33% interest of a structure with an initial cost of $366,653 and annual operating and maintenance costs of $66,265, commencing 7 years after the construction of the structure.

36. Determine the capitalized cost at 9.55% interest of a structure with an initial cost of $450,056 and annual operating and maintenance costs of $63,216, commencing 5 years after the construction of the structure. ( answer :1119519.103, double check!!)


38. How much money will you at present time if you deposit P9,255 each for the next 9 years in a savings account that earns 6% compounded quarterly ? (answer: 255999.63, double check!)
39. Find the accumulated amount of P3,609 invested 0.07% compound daily at for a period of 12 years.

40. Find the accumulated amount of P3,389 for 4 years and 8 months at 9.4% simple interest. (answer :4875.64, double check!!)


41. Find the weekly yield (in %) for an investment that has a interest rate of 9.06% compounded quarterly

42. If you can earn 11.6% on your investments yearly, and you would like to accumulate P293,813 for your savings at the end of 13 years, how much must you invest annually to reach your goal? (answer: 70540.17 ANO PO FORMULA?, double check!!)

43. A debt of $10,000 is amortized by making equal payments at the end of every six months for three years, and interest is 6% compounded semi-annually. Determine the interest ρáíd for 4th payment. (answer: 156.65, double check!!)

44. A debt of $10,000 is amortized by making equal payments at the end of every six months for three years, and interest is 6% compounded semi-annually. Determine the interest ρáíd for 4th payment.

 

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7. To find the weekly yield for an investment with an interest rate of 6.7% compounded quarterly, we need to convert the interest rate to a weekly rate.

First, we need to find the quarterly interest rate. We can use the formula:

(1 + r)^n = (1 + i)^m

Where r is the quarterly interest rate, i is the annual interest rate, n is the number of quarters in a year (4), and m is the number of years.

Plugging in the values, we have:

(1 + r)^4 = (1 + 0.067)^1

Simplifying, we get:

(1 + r)^4 = 1.067

Taking the fourth root of both sides, we have:

1 + r = 1.067^(1/4)

Solving for r, we get:

r = 1.067^(1/4) - 1

r ≈ 0.0166

Now, we need to find the weekly interest rate. Since there are 52 weeks in a year, we divide the quarterly interest rate by 13 (52/4):

Weekly interest rate = 0.0166 / 13 ≈ 0.0013

To express the weekly interest rate as a percentage, we multiply by 100:

Weekly yield ≈ 0.0013 * 100 = 0.13%

Therefore, the weekly yield for an investment with an interest rate of 6.7% compounded quarterly is approximately 0.13%.

8. To find the accumulated amount of P3,001 for 5 years and 8 months at 5.9% simple interest, we can use the formula:

Accumulated amount = Principal + (Principal * Interest rate * Time)

First, we need to convert the time period to years. 8 months is equal to 8/12 = 2/3 years.

Plugging in the values, we have:

Accumulated amount = 3001 + (3001 * 0.059 * (5 + 2/3))

Simplifying, we get:

Accumulated amount = 3001 + (3001 * 0.059 * (17/3))

Accumulated amount ≈ 3001 + (3001 * 0.059 * 5.6667)

Accumulated amount ≈ 3001 + (3001 * 0.3354)

Accumulated amount ≈ 3001 + 1006.95

Accumulated amount ≈ 4007.95

Therefore, the accumulated amount of P3,001 for 5 years and 8 months at 5.9% simple interest is approximately P4,007.95.

9. To find the time (in years) for a P30,000 deposit to triple itself at 5% compounded monthly, we can use the formula:

Final amount = Principal * (1 + Interest rate)^Time

We need to find the time it takes for the deposit to triple, so the final amount would be 3 times the principal.

Plugging in the values, we have:

3 * P30,000 = P30,000 * (1 + 0.05/12)^(12*Time)

Dividing both sides by P30,000, we get:

3 = (1 + 0.05/12)^(12*Time)

Taking the logarithm of both sides, we have:

log(3) = log((1 + 0.05/12)^(12*Time))

Using the logarithmic property, we can bring down the exponent:

log(3) = (12*Time) * log(1 + 0.05/12)

Dividing both sides by (12 * log(1 + 0.05/12)), we get:

Time = log(3) / (12 * log(1 + 0.05/12))

Using a calculator, we find:

Time ≈ 7.144

Therefore, it takes approximately 7.144 years for a P30,000 deposit to triple itself at 5% compounded monthly.

14. To find the accumulated amount of P3,609 invested at 0.07% compound daily for a period of 12 years, we can use the formula:

Accumulated amount = Principal * (1 + Interest rate)^(n * Time)

Plugging in the values, we have:

Accumulated amount = 3609 * (1 + 0.0007)^(365 * 12)

Using a calculator, we find:

Accumulated amount ≈ 3609 * (1.0007)^(4380)

Accumulated amount ≈ 3609 * 1.3309

Accumulated amount ≈ 4800.4441

Rounding off to 4 decimal places, we get:

Accumulated amount ≈ 4800.4441

Therefore, the accumulated amount of P3,609 invested at 0.07% compound daily for a period of 12 years is approximately P4,800.4441.

17. To find the weekly yield for an investment with an interest rate of 5.22% compounded quarterly, we can follow the same steps as in problem 7.

First, we need to find the quarterly interest rate:

(1 + r)^4 = (1 + 0.0522)^1

Solving for r, we get:

r = 1.0522^(1/4) - 1

r ≈ 0.0128

Now, we need to find the weekly interest rate:

Weekly interest rate = 0.0128 / 13 ≈ 0.000987

To express the weekly interest rate as a percentage, we multiply by 100:

Weekly yield ≈ 0.000987 * 100 = 0.0987%

Therefore, the weekly yield for an investment with an interest rate of 5.22% compounded quarterly is approximately 0.0987%.

18. To find the accumulated amount of P4,731 for 4 years and 8 months at 9.9% simple interest, we can use the formula:

Accumulated amount = Principal + (Principal * Interest rate * Time)

First, we need to convert the time period to years. 8 months is equal to 8/12 = 2/3 years.

Plugging in the values, we have:

Accumulated amount = 4731 + (4731 * 0.099 * (4 + 2/3))

Simplifying, we get:

Accumulated amount = 4731 + (4731 * 0.099 * (14/3))

Accumulated amount ≈ 4731 + (4731 * 0.099 * 4.6667)

Accumulated amount ≈ 4731 + (4731 * 0.463)

Accumulated amount ≈ 4731 + 2189.953

Accumulated amount ≈ 6920.953

Therefore, the accumulated amount of P4,731 for 4 years and 8 months at 9.9% simple interest is approximately P6,920.953.

19. To find the amount of money that should be invested in an account that earns 7.5% interest, compounded quarterly, in order to have P100,000 in 8 years, we can use the formula:

Accumulated amount = Principal * (1 + Interest rate)^Time

We need to find the principal amount, so we can rearrange the formula as:

Principal = Accumulated amount / (1 + Interest rate)^Time

Plugging in the values, we have:

Principal = 100000 / (1 + 0.075/4)^(4*8)

Using a calculator, we find:

Principal ≈ 100000 / (1.01875)^(32)

Principal ≈ 100000 / 1.765

Principal ≈ 56609.497

Therefore, approximately P56,609.50 should be invested in an account that earns 7.5% interest, compounded quarterly, in order to have P100,000 in 8 years.

23. To find the amount that must be invested annually to accumulate P251,453 at the end of 15 years with an annual interest rate of 11.8%, we can use the formula for the future value of an annuity:

Future value of annuity = Annual payment * [(1 + Interest rate)^Number of periods - 1] / Interest rate

Plugging in the values, we have:

251453 = Annual payment * [(1 + 0.118)^15 - 1] / 0.118

Simplifying, we get:

251453 * 0.118 = Annual payment * [(1.118)^15 - 1]

Annual payment = (251453 * 0.118) / [(1.118)^15 - 1]

Using a calculator, we find:

Annual payment ≈ 70540.17

Therefore, approximately P70,540.17 should be invested annually to accumulate P251,453 at the end of 15 years with an annual interest rate of 11.8%.

26. The question is a duplicate of question 19. Please refer to the answer provided for question 19.

28. To find the final value if you invest P33,742 into a certificate of deposit that has an annual interest rate of 9.5% compounded quarterly for 4 years, we can use the formula for compound interest:

Final value = Principal * (1 + Interest rate/Number of compounding periods)^(Number of compounding periods * Time)

Plugging in the values, we have:

Final value = 33742 * (1 + 0.095/4)^(4 * 4)

Using a calculator, we find:

Final value ≈ 49121.71

Therefore, the final value of the investment would be approximately P49,121.71.

31. To find the accumulated amount of P4,928 invested at 0.1% compound daily for a period of 13 years, we can use the formula:

Accumulated amount = Principal * (1 + Interest rate)^(n * Time)

Plugging in the values, we have:

Accumulated amount = 4928 * (1 + 0.001)^(365 * 13)

Using a calculator, we find:

Accumulated amount ≈ 4928 * (1.001)^(4745)

Accumulated amount ≈ 4928 * 1.6059

Accumulated amount ≈ 7913.4821

Rounding off to 4 decimal places, we get:

Accumulated amount ≈ 7913.4821

Therefore, the accumulated amount of P4,928 invested at 0.1% compound daily for a period of 13 years is approximately P7,913.4821.

32. To find the accumulated amount of P4,425 for 3 years and 8 months at 8.8% simple interest, we can use the formula:

Accumulated amount = Principal + (Principal * Interest rate * Time)

First, we need to convert the time period to years. 8 months is equal to 8/12 = 2/3 years.

Plugging in the values, we have:

Accumulated amount = 4425 + (4425 * 0.088 * (3 + 2/3))

Simplifying, we get:

Accumulated amount = 4425 + (4425 * 0.088 * (11/3))

Accumulated amount ≈ 4425 + (4425 * 0.088 * 3.6667)

Accumulated amount ≈ 4425 + (4425 * 0.3233)

Accumulated amount ≈ 4425 + 1430.7425

Accumulated amount ≈ 5855.7425

Therefore, the accumulated amount of P4,425 for 3 years and 8 months at 8.8% simple interest is approximately P5,855.7425.

34. To find the final value if you invest P23,367 into a certificate of deposit that has an annual interest rate of 10.1% compounded quarterly for 5 years, we can use the formula for compound interest:

Final value = Principal * (1 + Interest rate/Number of compounding periods)^(Number of compounding periods * Time)

Plugging in the values, we have:

Final value = 23367 * (1 + 0.101/4)^(4 * 5)

Using a calculator, we find:

Final value ≈ 38476.762

Therefore, the final value of the investment would be approximately P38,476.762.

35. To find the accumulated amount of P4,734 invested at 0.1% compound daily for a period of 18 years, we can use the formula:

Accumulated amount = Principal * (1 + Interest rate)^(n * Time)

Plugging in the values, we have:

Accumulated amount = 4734 * (1 + 0.001)^(365 * 18)

Using a calculator, we find:

Accumulated amount ≈ 4734 * (1.001)^(6570)

Accumulated amount ≈ 4734 * 2.194

Accumulated amount ≈ 10380.996

Therefore, the accumulated amount of P4,734 invested at 0.1% compound daily for a period of 18 years is approximately P10,380.996.

36. To determine the capitalized cost at 7.33% interest of a structure with an initial cost of $366,653 and annual operating and maintenance costs of $66,265, commencing 7 years after the construction of the structure, we can use the formula for capitalized cost:

Capitalized cost = Initial cost + (Annual operating and maintenance costs / Interest rate) * (1 - (1 + Interest rate)^(-n))

Plugging in the values, we have:

Capitalized cost = 366653 + (66265 / 0.0733) * (1 - (1 + 0.0733)^(-7))

Using a calculator, we find:

Capitalized cost ≈ 366653 + (66265 / 0.0733) * (1 - 0.4804)

Capitalized cost ≈ 366653 + (66265 / 0.0733) * (0.