Question

A loan of $ 10000 is to be repaid in 30 equal monthly
installments with the first one paid seven months after the loan is
made. The nominal annual interest rate is 6 % compounded quarterly.
Determine the amount of the monthly payment.

Please show detailed process

Answer #1

First we have to convert the quarterly rate in EAR and than monthly compunded rate | |||||||

EAR = | (1+6%/4)^4-1 | 6.14% | |||||

Annual rate (Monthly compounding) = | ((1+6.41%)^(1/12)-1)*12 | ||||||

5.97% |
|||||||

Future value of the loan at the end of 6th month | |||||||

put in calculator | |||||||

PV | -10000 | ||||||

PMT | 0 | ||||||

I | 5.97%/12 | 0.4975% | |||||

N | 6 | ||||||

Compute FV | $10,302.25 | ||||||

Computation of monthly rate | |||||||

put in calculator | |||||||

FV | 0 | ||||||

PV | ($10,302.25) | ||||||

I | 0.4975% | ||||||

N | 30 | ||||||

Compute PMT | $370.53 | ||||||

Ans = |
$370.53 |

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