Question

If a mechanic uses his credit card to pay for a compressor that costs $477.95 and does not pay on it until the second month, what will the 1.5% monthly interest charge be at the end of the first month?

A. $7.17

B. $12.83

C. $15.43

D. $22.06

Answer 1

A. $7.17

Explanation:

We have been given that a mechanic uses his credit card to pay for a compressor that costs $477.95 and does not pay on it until the second month.

We will use compound interest formula to solve our given problem.

`A=P(1+(r)/(n))^(nT)` where,

A = Final amount after T years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Periods of compounding,

T = Time in years.

Let us multiply our given rate by 12 to get APR and convert it in decimal form.

`APR=12* 1.5\%`

`APR=18\%`

`18\%=(18)/(100)=0.18`

Since 1 year equals 12 months, so 1 month will be 1/12 year.

Upon substituting our given values in above formula we will get,

`A=477.95(1+(0.18)/(12))^{12*(1)/(12)}`

`A=477.95(1+0.015)^(1)`

`A=477.95(1.015)`

`A=485.11925`

Now let us subtract principal amount from the final amount to get the monthly interest charge at the end of 1st month.

`\text{The monthly interest charge be at the end of the first month}=485.11925-477.95`

`\text{The monthly interest charge be at the end of the first month}=7.16925\approx 7.17`

Therefore, the monthly interest charge be at the end of the first month will be $7.17 and option A is the correct choice.