Question

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment

Answer 1

Answer:

After first payment the amount remains$= 3807.1066 * 4 = 15228.4264$

Explanation:

The borrowed amount = $15000

The interest rate on borrowed amount = 8.5%

Repayment years = 5 years

Installment amount should be in five equal apart.

Now we have to find the annual payment amount (that is annuity ).

$15000 = \frac{A(1-(1+r)^{-n}}{r} \\15000 = \frac{ A(1-(1+ 0.085)^{-5}}{0.085}\\1275 = A(1-(1+ 0.085)^{-5}} \\1275 = 0.3349A \\A = 3807.1066$

Since it is given that amount is repaid in 5 equal installment. Thus installment amount is $3807.1066 and after 1st installment four installment have to be paid.

So after first payment the amount remains$= 3807.1066 * 4 = 15228.4264$