Use the compound interest formulas A=P (1+ r over n) squared nt and A=P e squared rt to solve the problem given. Round answers to the nearest cent.

Find the accumulated value of an investment of $25,000 for 6 years at an interest rate of 6.5% if the money is a. compounded? semiannually; b. compounded? quarterly; c. compounded? monthly; d. compounded continuously.

 

Answer:

a.)36696.17

b.)36808.95

c.)36885.68

d.)36924.52

Refer to the explanation part for complete solution.

Step-by-step explanation

Solution:

For all the subparts, P=$25000, r=0.065, and t=6 years.

a) Here, n=2. The amount accumulated will be:

Formula used:

A = P(1+ r/n)^nt

A = 25000(1 + 0.065/2)^2∗6 ≈ 36696.17

b) Here, n=4. The amount accumulated will be:

Formula used:

A = P(1+ r/n)^nt

A = 25000(1 + 0.065/4)^4∗6 ≈ 36808.95

c) Here, n=12. The amount accumulated will be:

Formula used:

A = P(1+ r/n)^nt

A = 25000(1 + 0.065/12)^12∗6 ≈ 36885.68

d) Using the second formula:

Formula used:

A = P*e^rt

A = 25000e^0.065∗6 ≈ $36924.52