Answer to Question #292982 in Financial Math for Ella

Question

A family needs a loan of 10 000 € for renovation. The loan period is 1 year and payments are made 4 times a year. The interest rate of the annuity loan is 4.2 % p.a. What is the remaining balance after the first payment?

Answer 1

The family takes a loan of 10,000.

We have the following information.

$n=4\\i={0.042\over4}=0.0105$ where, $n$ is the loan period and $i$ is the interest rate.

Let $P$ be the quarterly installment. So $P$ is given as,

$P={10,000\over{(1-1.0105^{-4})\over0.0105}}=2565.97$

$P=2565.97$ is also the amount payable in the first installment.

The total payment after the 4 times of payment is, $2565.97\times 4=10263.87$

So the remaining balance after the first payment is, $10263.87-2565.97=7697.90$