Question

You have just received an offer in the mail from Friendly Loans. The company is offering to loan you $4,750 with low monthly payments of $100 per month. If the interest rate on the loan is an APR of 15.5 percent compounded monthly, how long will it take for you to pay off the loan

Answer 1

Answer:

It will take 74 months to pay-off the loan

Explanation:

We need to find time (n) in the present value of an annuity

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  $100.00

time n

rate 0.012916667(0.155 / 12 months)

PV $4,750.00

$100 \times \frac{1-(1+0.01291667)^{-n} }{0.01291667} = 4750$

$(1+0.01291667)^{-n}= 1-\frac{4750\times0.0129167}{100}$

$(1+0.01291667)^{-n} = 0.38645833$

Now, we solve for n using logarithmics properties:

$-n= \frac{log0.38645833}{log(1+0.01291667)$

-n =  -74.07934663

n = 74