Question

Larry accumulated $3,000 in credit card debt. If the interest rate is 10% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years for quarterly compounding?

Answer 1

• The debt amount is $3,000.

,

• The interest rate is 10% per year.

,

• The period of time is 2 years.

,

• The compound is monthly.

The interest compound formula is

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

Where P = 3,000, r = 0.10, n = 4, and t = 2.

Notice that n = 4 because the interest is quarterly compound.

Let's replace the values and solve them.

`\begin{gathered} A=3,000(1+(0.10)/(4))^(4\cdot2) \\ A=3,000(1+0.025)^8 \\ A=3,000(1.025)^8 \\ A=3,000(1.22)\approx3655.21 \end{gathered}`

Therefore, Larry will owe $3,655.21.