Question

Brian borrows $15,000 from Mary and agrees to repay with 12 installments payable half-yearly. The effective interest rate is 6.09% per annum. When the 6th payment is due, Brian repays the outstanding loan balance by a lump sum.

a.) Calculate the lump sum payment of Brian

b.) Calculate the loss of interest income of Mary

Please show all work by hand, without using a finance calculator or Excel. Thank you.

Answer 1

First we calculate the monthly payments PMT

Let the semi-annual rate be r, then

(1+r)^2 = (1+6.09%)

(1+r) = 1.03

r = 3%

PV = 15000

n = 12

15000 = PMT*[(1-(1+0.03)^(-12))/0.03]

PMT = $1506.93

a)

Lump sum payment = PV of all the future payments after 6th installments + 6th installment due

+ 1506.93

Lump sum payment = 1506.93*[(1-(1+0.03)^(-6))/0.03]+1506.93

Lump sum payment = $9670.26

b)

Loss of interest = Total 12 payments expected at the start of loan - Total 5 installments and the lumpsum payment

Loss of interest = 12*1506.93 - (5*1506.93+9670.26)

Loss of interest = $878.25