Question

How much would a bank be willing to loan if the borrower offered terms of repaying $1,000 every six months for 40 years (i.e. first payment is made 6 months from today, the second payment is made one year from today, etc.) and the relevant rate of interest is 5% APR, compounded semiannually?

Answer 1

Answer : Calculation of the amount bank be willing to loan if the borrower offered terms of repaying $1,000 every six months for 40 years :

In this case we need to calculate present value of payments :

Using Excel function of PV

=PV(rate,nper,pmt,fv)

where

rate is the rate of interest per period i.e 5% / 2 = 2.5%(Divided by 2 as given that interest are compounded semiannually)

nper is the number of payments i.e 40 * 2 = 80 (Multiplied by 2 as given that interest are compounded semiannually)

pmt is the periodic repayment i.e $1000

fv is the future value i.e 0

=PV(2.5%,80,-1000,0)

On putting these values in PV function of Excel

Amount bank be willing to loan if the borrower offered terms of repaying $1,000 every six months for 40 years = 34,451.82