Aimee Walters has a choice for her investment of 4,000. She can invest it in either (a) an account that pays 10% with compound interest for 2 years or (b) an account that pays 10% with simple interest for 2 years. Find the future value of both. Which is larger?

A. The simple interest account earns 400 more in two years than the compound interest account.

B. The compound interest account earns 40 more in two years than the simple interest account.

C. The simple interest account earns 40 more in two years than the compound interest account.

D. The compound interest account earns 400 more in two years than the simple interest account.

Guest Feb 14, 2021

#1**0 **

She has 4,000 dollars.

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

where,

A = final amount

P = initial investment

r = interest rate

n = number of times interest is applied

t = number of time periods

Case A:

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

^{ }= 4000(1 + 0.1/1)^{(1*2)}

= 4000(1.1)^{2}

= 4000 * 1.21

= $4840.00

A = P(1 + rt)

where,

A = final amount

P = initial investment

r = interest rate

t = time in years

Case B:

A = P(1 + rt)

= 4000(1 + 0.1*2)

= 4000 * 1.2

= $4800.00

4840 - 4800 = 40, which means your answer is B) The compount interest account earns 40 more in two years than the simple interest account.

Hope this helps :)

Logarhythm Feb 14, 2021