Question

Tom accumulated $12,000 in credit card debt. If the interest rate is 4% per year and he does not make any payments for 8 years, how much will he owe on this debt in 8 years by compounding continuously? Round to the nearest cent

Answer 1

$16422.83

Explanation:

Given that:

Debt in credit card = $12000

Interest rate = 4%

Time for which Tom does not make any payment = 8 years

The debt is compounding annually.

To find:

The total debt = ?

Solution:

This problem is nothing but a problem of compound interest in which we have to find the amount after 8 years compounding annually at a rate of 4% for the principal amount of $12000.

So, Principal, P = $12000

Rate of interest, R = 4%

Time, T = 8 years

Formula for Amount is given as:

`A = P(1+(R)/(100))^T`

Putting all the given values:

`A = 12000(1+(4)/(100))^8\\\Rightarrow A = 12000(1+0.04)^8\\\Rightarrow A = 12000(1.04)^8\\\Rightarrow A = 12000* 1.36856905\\\Rightarrow A = \$16422.83`

So, the Tom owes a total of $16422.83 after 8 years.