Question

9 years ago you borrowed $147695 to buy a house. The interest rate quoted to you was 6.26 percent for 30 years with monthly payments. Assuming you have made regular monthly payments up to now, what is the amount (in $) you still owe on the loan today? Answer to two decimals.

Hint: The hard way to do this is to use an amortization table. There is an easier way - see if you can find it.

Can you explain how to do this on a financial calculator? What would you type in and where.

Answer 1

Step 1 - Find out the monthly loan payment
We can use the present value of annuity formula to calculate the monthly loan payment.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan borrowed = $147695
P = monthly loan payment = ?
r = monthy interest rate = 6.26%/12 = 0.005217
n = number of monthly loan payments = 30 years * 12 = 360
147695 = P x {[1 - (1+0.005217)^-360]/0.005217}
147695 = P x 162.2408103
P = 910.34
Monthly loan payment = $910.34
Step 2 - Find out the loan amount you still owe today.
We can use the present value of annuity formula to calculate the today's loan outstanding.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = amount you still owe on the loan today = ?
P = monthly loan payment = 910.34
r = monthy interest rate = 6.26%/12 = 0.005217
n = number of monthly loan payments remaining = 21 years * 12 = 252
Present value of annuity = 910.34 x {[1 - (1+0.005217)^-252]/0.005217}
Present value of annuity = 910.34 x 140.03
Present value of annuity = 127477.10
You still owe $1,27,477.10 on the loan today.