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1) If you take out a bank loan of $25000 now, at a quoted annual rate of 7
1) If you take out a bank loan of $25000 now, at a quoted annual rate of 7.5% compounded monthly, how much would the monthly payments be if the loan must be repaid with equal monthly installments over the next 4 years?
2) Tracy Chapman is saving to buy a house in five years. She plans to put 20 percent down at that time, and she believes that she will need $35,000 for the down payment. If Tracy can invest in a fund that pays 9.25 percent annual interest, compounded quarterly, how much will she have to invest today?
Expert Solution
1) We can calculate the monthly installments by using the following formula in excel:-
=pmt(rate,nper,-pv,fv)
Here,
Pmt = Monthly installments
Rate = 7.5%/12 = 0.625% (monthly)
Nper = 4*12 = 48 periods (monthly)
PV = $25,000
FV = $0
Substituting the values in formula:
= pmt(0.625%,48,-25000,0)
= $604.47
2) Computation of the present value:-
FV = PV*(1+rate)^n
Here,
n = 5*4 = 20 periods (quarterly)
Rate = 9.25%/4 = 2.3125% (quarterly)
$35,000 = PV*(1+2.3125%)^20
PV = $35,000 / 1.5797
= $22,156.14
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