Question

Use the compound interest formulas Upper A equals Upper P left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript nt and Upper A equals Pe Superscript rt to solve the problem given.

Round answers to the nearest cent.

Find the accumulated value of an investment of $ 10 comma 000 for 7 years at an interest rate of 7 % if the money is :

a. compounded​semiannually;

b. compounded​ quarterly;

c. compounded monthly

d. compounded continuously.



a. What is the accumulated value if the money is compounded​ semiannually? ​$ nothing ​(Round your answer to the nearest​ cent.)

b.What is the accumulated value if the money is compounded​ quarterly? ​$ nothing ​(Round your answer to the nearest​ cent.)

c. What is the accumulated value if the money is compounded​ monthly? ​$ nothing ​(Round your answer to the nearest​cent.)

d. What is the accumulated value if the money is compounded​continuously? ​$ nothing ​(Round your answer to the nearest​cent.)

Answer 1

Explanation:

Initial amount deposited into the account is $10000 This means that the principal, P = 10000

The rate at which the principal was compounded is 7%. So

r = 7/100 = 0.07

It was compounded for 7 years. So

t = 7

The formula for compound interest is

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

A = total amount in the account at the end of t years.

a) compounded ​semi annually

It means that it was compounded twice in a year, so n = 2

Therefore

A = 10000 (1+0.07/2)^2×7

A = 10000(1.035)^14 = $16186.9

b) compounded​ quarterly

It means that it was compounded four times in a year, so n = 4

Therefore

A = 10000 (1+0.07/4)^4×7

A = 10000(1.0175)^28 = $16254.1

c) compounded monthly

It means that it was compounded 12 times in a year, so n = 12

Therefore

A = 10000 (1+0.07/12)^12×7

A = 10000(1.0058)^84 = $16254.6

d) compounded continuously

A = Pe^Rt

A = 10000e^7×0.07 = 10000×e^0.49

A = $16323.2