Question

Five years ago you borrowed $250,000 for a ten-year period at a fixed interest rate of 9% p.a. with interest compounded on an annual basis. You have been making regular annual payments on your loan and you now wish to repay the amount outstanding on this loan in full. The total amount you need to repay today is closest to:

$151,521.

$168,850.

$194,775.

$217,051.

Answer 1

Solution

Answer-$151,521.

Present value of Annuity ordinary annuity=Annuity payment*((1-(1/(1+r)^n))/r)

where

r-intrest rate per period-9%

n-number of periods-10

Present value of Annuity=250000

250000=Annuity payment*((1-(1/(1+.09)^10))/.09)

Solving

Annuity payment=$38,955.02

Now the Present value of 5 annuity payments made for 5 years=38955.02*((1-(1/(1+.09)^5))/.09)

=151521.4

Thus Present value to be covered by 1 payment=250000-151521.4

=98478.6

Now

Future value to be made in 5 years to close the loan=Presnt value to be covered in lumpsum*(1+r)^n

where

r-intrest rate-9%

n-number of periods-5

Future value to be made in 5 years to close the loan=98478.6*(1+.09)^5

=151521.5

Thus correct answer is 151521

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