Question

Charles must make a loan payment of $1,620 at the end of each quarter. His nominal...

Charles must make a loan payment of $1,620 at the end of each quarter. His nominal annual loan rate is 5%, compounded quarterly. The original term of the loan was 13 years. How much did Charles originally borrow?

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Answer #1

Answer

the effective interest rate per quarter =nominal annual rate /number of compounding

=5/4

=1.25%=i=r

n=number of quarters =13*4=52

A=quaterlly payment =1620

PV=present value = originally borrowed amount

PV=A*(P|A,i,n)

PV=1620*(P|A,1.25%,52)

PV=1620*38.06773431135646

=61669.7296

the amount is $61669.73

=======

or

by formula

PV = A1-(411) PV = 1620 * 1 – (1+0.0125) 52 0.0125 PV = 61669.72958

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