Question

Deshaun wants to borrow 551,000 from the bank and is choosing among two possible loans. The interest rate on both loans is 2.90 percent per quarter. Loan A would require him to make 48 equal quarterly payments, with the first payment made to the bank in 3 months. Loan B would also require him to make equal quarterly payments to the bank. However, 1) the quarterly payment associated with loan B would be $132 less than the quarterly payment associated with loan A and 2) the first quarterly payment for loan would be made to the bank later today. How many quarterly payments to the bank must be made with loan B? a. 56.25 (plus or minus 0.50) b. 45.21 (plus or minus 0.50) c. 52.52 (plus or minus 0.50) d. 60.90 (plus or minus 0.50) e. None of the other alternatives is within 0.50 of the correct answer

Answer 1

First, we calculate the quarterly payment for Loan A.

Quarterly loan payment is calculated using PMT function in Excel :

rate = 2.9% (quarterly rate)

nper = 48 (total number of payments)

pv = 51000 (loan amount)

PMT is calculated to be $1,981.38

A1 =PMT(2.9%,48,51000)*-1 B с D E F A $1,981.38 1

Quarterly payment for Loan B =  $1,981.38 = $132 = $1,849.38

Number of quarterly payments for Loan B is calculated using NPER function in Excel ;

rate = 2.9% (quarterly rate)

pmt = -1849.38 (quarterly payment)

pv = 51000 (loan amount)

fv = 0 (loan balance at end of payments is zero)

type = 1 (first payment is made today, hence it is an annuity due)

NPER is calculated to be 52.52

With Loan B, 52.52 quarterly payments must be made

A3 х =NPER(2.9%,-A2,51000,0,1) B с D E F A 2 $1,849.38 3 52.52 3

The answer is (c)