Question

Six years ago, you borrowed $200,000 for a ten-year period from BOB Bank at a stated interest rate of 10% p.a. with interest compounded quarterly. You have been making equal, quarterly payments on the loan during this time and now wish to repay the loan in full. The amount that you need to repay the bank today is closest to:

Group of answer choices

$142,494.

$72,524.

$104,012.

$187,678.

Answer 1

Amount borrowed = 200000

No of quarters= n= 10*4= 40

Rate= r= 10%/4= 2.5% per quarter

First we need to find the quarterly payment which is P

Amount borrowed = P*(1-1/(1+rate)^number of terms)/rate

200000= P*(1-1/(1+2.5%)^40)/2.5%

200000= P*25.10278

P= 7967.25

Next we find the present value of payments remaining

Payment=P= 7967.25

No of payments remaining= n= 4 years*4= 16

Rate=r= 2.5%

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

= 7967.25*(1-1/(1+2.5%)^16)/2.5%

= 7967.25*13.055

= 104012.43

Option 3 $104,012. is the right option