Question

# A loan of \$6,300 is being repaid by payments of \$70 at the end of each...

A loan of \$6,300 is being repaid by payments of \$70 at the end of each month. After the 7th payment, the payment size increases to \$280 per month. If the interest rate is 6.6% compounded monthly calculate the outstanding loan balance at the end of the first year.

Loan amount (present value) =6300

interest rate per month (i) =6.6%/12 =0.0055

number of months (n) =12

future value of loan at end of year 1 = PV*(1+i)^n

=6300*(1+0.0055)^12

=6728.611425

Payment of \$70 per month is increased to payment of 280 per month after 7th payment

So we segreggate it into two annuiities.

first annuity \$70 for 12 months

second annuity \$210 for 5 months

We will find future value of both annuities and subtract from loan value future value to find loan balance at end of year 1

Future value of annuity formula =annuity *(((1+i)^n)-1)/i

FV of \$70 annuity = 70*(((1+0.0055)^12)-1)/0.0055

=865.881666

FV of \$210 annuity =210*(((1+0.0055)^5)-1)/0.0055

=1061.6137

Loan balance = FV of loan - FV of both annuities payment

= 6728.611425-865.881666-1061.6137

=4801.116059

So loan balance at end of year 1 is \$4801.12

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