Question

Yvette is considering taking out a loan with a principal of $16,200 from one of two banks. Bank F charges an interest rate of 5.7%, compounded monthly, and requires that the loan be paid off in eight years. Bank G charges an interest rate of 6.2%, compounded monthly, and requires that the loan be paid off in seven years. How would you recommend that Yvette choose her loan? a. Bank F offers a better loan in every regard, so Yvette should choose it over Bank G’s. b. Yvette should choose Bank F’s loan if she cares more about lower monthly payments, and she should choose Bank G’s loan if she cares more about the lowest lifetime cost. c. Yvette should choose Bank G’s loan if she cares more about lower monthly payments, and she should choose Bank F’s loan if she cares more about the lowest lifetime cost. d. Bank G offers a better loan in every regard, so Yvette should choose it over Bank F’s.

Answer 1

Hi there
First find the monthly payment of each offer to see which monthly payment is lower
The formula of the present value of annuity ordinary is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value
PMT monthly payment
R interest rate
K compounded monthly 12
N time
Solve the formula for PMT
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]

Bank F
PMT=16,200÷((1−(1+0.057÷12)^(
−12×8))÷(0.057÷12))
=210.53

Bank G
PMT=16,200÷((1−(1+0.062÷12)^(
−12×7))÷(0.062÷12))
=238.21

From the above the monthly payment of bank f is lower than the bank g
And since the lifetime of bank g is lower than bank f the answer is
b. Yvette should choose Bank F’s loan if she cares more about lower monthly payments, and she should choose Bank G’s loan if she cares more about the lowest lifetime cost.

Good luck!