Question

Loan payment Determine the equal, end-of-year payment required each year over the life of the loans shown in the following table to repay them fully during the stated term of the loan.
Loan    Principal    Interest rate    Term of loan (years)
A    $12,000       8%       3
B       60,000    12     10
C       75,000    10     30
D         4,000    15        5

Answer 1

Equal year end payment can be calculated using PV formula of annuity,

PMT = PV*r/(1 - (1+r)^-t)

where PMT is yearly payment

PV = principal

r = interest rate

t = term of loans in years

So, For Loan A, yearly payment PMT = 12000*0.08/(1 - 1.08^-3) = $4656.40

For Loan B. yearly payment PMT = 60000*0.12/(1 - 1.12^-10) = $10619.05

For Loan C, yearly payment PMT = 75000*0.1/(1 - 1.1^-30) = $7955.94

For Loan D, yearly payment PMT = 4000*0.15/(1 - 1.15^-5) = $1193.26