Question

Narelle borrows $600,000 on a 25-year property loan at 4 percent per annum compounding monthly. The loan provides for interest-only payments for 5 years and then reverts to principal and interest repayments sufficient to repay the loan within the original 25-year period. Assume rates do not change.

a) Calculate the monthly repayment for the first 5 years. (CLUE: it is INTEREST ONLY)

b) Calculate the new monthly repayment after 5 years assuming the interest rate does not change. (You need the repayment required to amortise the loan to $0 in remaining 20 years)

c) Calculate the total repayments over the life of the loan.

d) Has she paid more or less than she would have if she took a principal and interest loan at the outset? Demonstrate showing your workings.

e) Why might she choose interest-only loan terms?

PLEASE EXPLAIN ANSWER WITHOUT CALCULATING FROM EXCEL

Answer 1

Part (a):

During the first 5 years, only interest need be paid. Hence monthly payments constitute only the monthly interest

Monthly interest= P*R/12 Where P= Principal and R= Yearly rate of interest

Given, Principal (P)= $600,000. Interest rate (R ) = 4%

Therefore, monthly payment during first 5 years= $600,000*4%/12= $2,000

Part (b):

Monthly payment during the remaining 20 years.

Monthly payments (PMT) is calculated using the formula PMT=[P*r*(1+r)^n]/[(1+r)^n]-1

Where P= Principal (loan amount), n= Number of installments and r= Rate of interest per month in decimals

Given,

Principal (P)= $600,000. Remaining period (number of months)= 20*12= 240.

Monthly interest rate (r )= 4%/12= 0.003333

Monthly payments= $600,000*0.003333*(1+0.003333)^240/(1+0.003333)^240)-1

=$600,000*0.003333*2.22258209/1.22258209 = 4445.16417/1.22258209 = $3,635.88

Part (c):

Total payments over the life of the loan= Interest payments during the first 60 months (part a) plus level payments during the remaining 20 years (part b)

=$2,000*60 + $3,635.88*240 = $ 120,000 + $ 872,611.67 = $ 992,611.67

Part (d):

Monthly payments if she took principal and interest loan at the outset

=$600,000*0.003333*(1+0.003333)^300/(1+0.003333)^300)-1

=$600,000*0.003333*2.71376516/1.71376516 = 5427.53032/3167.02104 = $ 3,167.02

Total payments if she took principal and interest loan at the outset

= $ 3,167.02*300= $ 950,106.31

Total payment in the option of interest only during first 5 years (part c above)= $ 992,611.67

This shows that she would have paid less if she opted principal and interest at the outset

Part (e):

She might choose interest only loan terms for the initial period because of liquidity constraints in the beginning. Interest only loan calls for only lower payments during that period.