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Six years ago, you borrowed $200,000 for a ten-year period from BOB Bank at a stated interest rate of 10% p
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.
Expert Solution
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
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