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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
Expert Solution
a. Computation of Effective Annual Interest Rate:
Effective Annual Interest Rate = (1 + Weekly Interest Rate)^Number of Weeks - 1
Here,
Weekly Interest Rate = Weekly Payment / Loan = $12.1101/$9,300 = 0.13%
Number of Weeks = 52
Effective Annual Interest Rate = (1 + 0.13%)^52 - 1
= 1.07000 - 1
Effective Annual Interest Rate = 0.07000 or 7%
b. Computation of Weekly Deposits using PMT Function in Excel:
=pmt(rate,nper,pv,-fv)
Here,
PMT = Weekly Deposits = ?
Rate = 5%/52 = 0.0962%
Nper = 52 Weeks * 10 Years = 520 Weeks
PV = 0
FV = $9,300
Substituting the values in formula:
=pmt(0.0962%,520,0,-9300)
PMT or Weekly Deposits = $13.79%
c. Computation of Monthly Deposits using PMT Function in Excel:
=pmt(rate,nper,pv,-fv)
Here,
PMT = Monthly Deposits = ?
Rate = 5%/12 = 0.417%
Nper = 12 Months * 10 Years = 120 Months
PV = 0
FV = $9,300
Substituting the values in formula:
=pmt(0.0417%,120,0,-9300)
PMT or Weekly Deposits = $59.89
d. Answer in Part C / Answer in Part B = $59.89 / $13.79 = 4.34 times
Thus the given statement is True
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