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

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