Question

Charles must make a loan payment of $1,989 at the end of each quarter. His nominal annual loan rate is 3%, compounded quarterly. The original term of the loan was 12 years. How much did Charles originally borrow?

Answer 1

Answer

the Amount is present value of the cahs flow.

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

i=quaterly interest rate =nominal annual /number of compounding =3/4=0.75%

n=number of quaters =12*4=48

A=quaterly payment =1989

PV=1989*(P|A,0.75%,48)

PV=1989*40.18478188517996

PV=79927.5312

the value is $79927.5312

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By formula

$PV = A[\frac{{1-(\frac{1}{1+r})^n}}{r}]\\ PV=1989*\frac{1-{(\frac{1}{1+0.0075})^{48}}}{0.0075}\\ PV=$ 79927.53117$