Question

Problem 2.7 Annual deposits earning monthly interest Given: You wish to buy a building with monthly payments of $1500 and a $20,000 downpayment. The bank offers a 30-year loan at 5.75% interest compounded monthly. Find: The maximum building price that you can afford

Answer 1

Monthly payment = $ 1500

Down payment = $ 20,000

Loan tenure = 30 years = 360 months

Interest rate = 5.75% = 0.479% per month

The present value of the loan can be written as

$\large PV = \frac{A}{1+i} +....+\frac{A}{(1+i)^n}$

$\large PV = \frac{A}{i}[1-\frac{1}{(1+i)^n}]$

$\large PV = \frac{1500}{0.00479}[1-\frac{1}{(1+0.00479)^{360}}]$

$\large PV = \frac{1500}{0.00479}*(1-0.178908)$

$\large PV = \frac{1500}{0.00479}*0.812091$

PV = $ 1,500 * 171.3582

PV = $ 257,037 (Approximately).

Maximum price = $ 20,000 + $ 257,037 = $ 277,037.

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