Question

You have just received an offer in the mail from Friendly Loans. The company is offering to loan you $5,000 with low monthly payments of $150 per month. If the interest rate on the loan is an APR of 16.1 percent compounded monthly, how long will it take for you to pay off the loan? Multiple Choice a. 47.90 months b. 44.48 months c. 33.33 months d. 41.51 months

Answer 1

Answer:

b. 44.48 months

Explanation:

We need to sovle for n in a common annuity:

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

C  $150.00

time n

rate 0.013416667 (0.161 / 12 months per year)

PV $5,000.0000

$150 \times \frac{1-(1+0.0134167)^{-n} }{0.0134167} = 5000$

$(1+0.0134167)^{-n}= 1-\frac{5000\times0.0134167}{150}$

$(1+0.0134167)^{-n}= 0.55277778$

We solve using logarithmics properties

$-n= \frac{log0.552777777777778}{log(1+0.0134166666666667)$

-n = -44.47953304

n = 44.48