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Donald plans to invest \(x\) dollars in a savings account that pays interest at an annual rate of \(8\%\) compounded

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Donald plans to invest \(x\) dollars in a savings account that pays interest at an annual rate of \(8\%\) compounded

by M7MBA » Fri Feb 19, 2021 7:24 am

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Donald plans to invest \(x\) dollars in a savings account that pays interest at an annual rate of \(8\%\) compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over \(\$100\) in interest within \(6\) months?

A. 1500
B. 1750
C. 2000
D. 2500
E. 3000

Answer: D

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Re: Donald plans to invest \(x\) dollars in a savings account that pays interest at an annual rate of \(8\%\) compounded

by Scott@TargetTestPrep » Tue Mar 09, 2021 1:27 pm
M7MBA wrote: ↑
Fri Feb 19, 2021 7:24 am
 Donald plans to invest \(x\) dollars in a savings account that pays interest at an annual rate of \(8\%\) compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over \(\$100\) in interest within \(6\) months?

A. 1500
B. 1750
C. 2000
D. 2500
E. 3000

Answer: D

Solution:

We can use the formula A = P(1 + r/n)^(nt) to solve this problem. Here P = x, r = 0.08, n = 4, and t = ½ since 6 months = ½ of a year, so nt = 4(½) = 2. Furthermore, let’s assume the interest in 6 months is exactly $100; thus A = x + 100. Therefore, we can create the following equation:

x(1 + 0.08/4)^2 = x + 100

x(1.0404) - x = 100

.0404x = 100

x = 100/.0404 ≈ 100/.04 = 2500

Answer: D

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