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Homework answers / question archive / Farid has a loan for $9300
Farid has a loan for $9300. He will make weekly payments (52 payments per year) of interest only for 6 years, and then his final payment will also include the initial amount of the loan.
a) If his weekly payments (except the last) are $12.1101, what is the effective annual interest rate?
Farid is planning to pay accumulate the money to pay off the loan by making regular deposits (at the end of each period) in a sinking fund paying an effective annual rate of 5% per year.
b) If he makes weekly deposits (52 weeks in a year), how much is each deposit?
c) If he makes monthly deposits, how much is each deposit?
d) The answer to part c) is more than 4 times the answer to part b).
True
False
a). Computation of the effective annual interest rate (EAR):-
Weekly interest rate = Weekly payment / Loan amount
= $12.1101 / $9,300
= 0.13%
Effective annual interest rate = (1 + Weekly interest rate)^n-1
= (1+0.13%)^52- 1
= 1.0700 - 1
= 7.00%
b). We can calculate the weekly deposits by using the following formula in excel:-
=pmt(rate,nper,pv,-fv)
Here,
Pmt = Weekly deposits
Rate = 5%/52 = 0.0962% (weekly)
Nper = 6*52 = 312 periods (weekly)
PV = 0
FV = $9,300
Substituting the values in formula:
= pmt(0.0962%,312,0,-9300)
= $25.57
c). We can calculate the monthly deposits by using the following formula in excel:-
=pmt(rate,nper,pv,-fv)
Here,
Pmt = Monthly deposits
Rate = 5%/12 = 0.4167% (monthly)
Nper = 6*12 = 72 periods (monthly)
PV = 0
FV = $9,300
Substituting the values in formula:
= pmt(0.4167%,72,0,-9300)
= $111.03
d). The answer to part c) is more than 4 times the answer to part b because;
Answer in Part C / Answer in Part B = $111.03 / $25.57
= 4.34 times
