Question

A loan has been issued for 7 years with a nominal interest rate of 8.1%, which is repaid with a periodic payment of 231 Eur at the beginning of each quarter. Need to determine the issued loan (in whole Eur)?

Answer 1

Annual rate - 8.1%

loan term - 7years

payment frequency - quarterly (number of payments in a year = 4)

periodic loan payment - 231Eur

periodic rate = $\frac{Annual rate }{ Number of payments in a year} = \frac{8.1}{4} = 2.025\%$

Number of payments = $Number of years * Number of payments in a year$ = 7 * 4 = 28

Loan amount = $\frac{periodic loan payment * (((1 + periodicrate)^{numberofpayments}) - 1)}{periodicrate * ((1 + periodicrate)^{numberofpayments}) } = \frac{231*((1 + 0.02025)^{28}-1)}{0.02025(1 + 0.02025)^{28}}$ =

4900.08 Eur

Total loan payment = $Number of payment * Periodic loan payment$ =

= 28 * 231 = 6468 Eur