Question

A person has a 10-year contract to receive a base salary of $25,000 a year and an increase of 5% every year starting from the second year. The person purchases a luxury item now for $43,000. The interest rate is 4% per year and the person would like to arrange a 10-year loan such that an equal amount of money will be available for consumption in each of the next 10 years. Calculate the amount to be borrowed and the amount paid back each year. (Assume that the salary is obtained at the end of each year, the loan is taken at the beginning of the first year and that loan payments are submitted at the end of each year.)

Explain verbally in detail and draw a timeline to illustrate.

Answer 1

Amount to be borrowed = $ 43000 as no downpayment is given

Particulars	Amount
Loan Amount	$             43,000.00
Int rate per Anum	4.0000%
No. of Years	10

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 43000 / PVAF (0.04 , 10)
= $ 43000 / 8.1109
= $ 5301.51

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods