Question

Kremena took out a

$500
discounted loan for a period of
3
months. The amount she actually received into her bank account was
$460
. Assuming simple interest rates, what is effective interest rate
r
e
? Give your answer as a percentage to the nearest percent. Do not include the percent symbol in your answer.

Answer 1

Answer:35

Explanation:

For this calculation we use the fact that the total interest is $500−$460=$40. Therefore using

I=Prt,

where r is the simple interest rate. We get

$40=$500×r×312.

Solving this for r gives r=0.32=32%. However the effective interest rate re will be higher. To calculate this, we use

A=L(1+ret).

Substituting the values A=$500,L=$460 (the loan drawdown amount from earlier), t=312 yields

500=460(1+312re),

and solving for re (see below) gives re≈0.3478, which is 35% to the nearest 1%.

500=460(1+312re)1.08696=1+312re(Dividebothsidesoftheequationby460.)0.08696=312re(Subtract1frombothsides.)1.04348=3re(Multiplybothsidesby12.)0.34783=re(Dividebothsidesby3.)