Question

Consider a loan for $100,000 to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 5% compounded annually. What is the remaining balance of the loan after 2 years ?

		$62,900
		$76,903
		$62,336
		$23,097
		$53,805

Answer 1

Option (a) is correct

First we will calculate the annual equal amount of the loan payment as per below:

Here, the payments will be same every year, so it is an annuity. For calculating annual payment, we will use the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity = $100000, P is the periodical amount , r is the rate of interest =5% and n is the time period = 5

Now, putting these values in the above formula, we get,

$100000 = P * (1 - (1 + 5%)^-5 / 5%)

$100000 = P * (1 - ( 1+ 0.05)^-5 / 0.05)

$100000 = P * (1 - ( 1.05)^-5 / 0.05)

$100000 = P * (1 - 0.78352616646) / 0.05)

$100000 = P * (0.21647383353 / 0.05)

$100000 = P * 4.32947667063

P = $100000 / 4.32947667063

P = $23097.48

So, annual payments are for $23097.48

At the end of year 1:

Interest = $100000 * 5% = $5000

Annual payment = $23097.48

Principal payment = $23097.48 - $5000 = $18097.48

Balance remaining = $100000 - $18097.48 = $81902.52

At the end of year 2:

Interest = $81902.52 * 5% = $4095.126

Annual payment = $23097.48

Principal payment = $23097.48 - $4095.126 = $19002.354

Balance remaining = $81902.52 - $19002.354 = $62900