Question

You borrow $100,000 and make annual payments for 5 years. The interest rate is 8%. How much interest do you pay in year 2?

PLEASE EXPLAIN STEP BY STEP HOW YOU SOLVE WITH ONLY YOUR FINANCIAL CALCULATOR

Answer 1

First we will calculate the annual payments. Here, the payments will be same every year, so it is an annuity. We will use the present value of annuity formula to calculate annual payments:

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 = 8% and n is the time period = 5

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

$100000 = P * (1 - (1 + 8%)^-5 / 8%)

$100000 = P * (1 - ( 1+ 0.08)^-5 / 0.08)

$100000 = P * (1 - ( 1.08)^-5 / 0.08)

$100000 = P * (1 - 0.68058319703) / 0.08)

$100000 = P * (0.31941680296 / 0.08)

$100000 = P * 3.99271003708

P = $100000 / 3.99271003708

P = $25045.65

So, annual payments are $25045.65.

Now,

Interest in year 1 = Amount borrowed / Outstanding * rate of interest

Interest in year 1 = $100000 * 8% = $8000

Principal repayment in year 1 = Annual payment - Interest in year 1

Principal repayment in year 1 = $25045.65 - $8000 = $17045.65

Principal outstanding at the end of year 1 = Amount borrowed - principal repayment

Principal outstanding at the end of year 1 = $100000 - $17045.65 = $82954.35

Interest in year 2 = Principal outstanding at the end of year 1 - rate of interest

Interest in year 2 = $82954.35 * 8% = $6636.35

So, interest in year 2 = $6636.35