Question
In: Finance
A construction company signed a loan contract at 4.07 % compounded semi-annually , with the provision...
A construction company signed a loan contract at 4.07 %
compounded semi-annually ,
with the provision to pay $665
at the end of each month
for three years.
(a) What is amount of the loan?
(b) How much will be owed at the end of seventeen
months?
(c) How much of the principal will be repaid within the first seventeen
months?
(d) How much interest is paid during the first seventeen
months?
Solutions
Expert Solution
| (a) | Loan amount | $ 22,511.88 | ||||||||
| Working: | ||||||||||
| # 1: Calculation of equivalent monthly interest rate | ||||||||||
| (1+i1)^n1 | = | (1+i2)^n2 | Where, | |||||||
| (1+i1)^6 | = | (1+0.02035)^1 | i1 | = | Monthly Interest rate | = | ? | |||
| (1+i1)^6 | = | 1.02035 | i2 | = | Semi annual interest rate | = | 4.07%/2 | = | 0.02035 | |
| 1+i1 | = | 1.02035 | ^(1/6) | |||||||
| 1+i1 | = | 1.00336326 | ||||||||
| i1 | = | 0.00336326 | ||||||||
| So, Equivalent monthly interest rate | = | 0.00336326 | ||||||||
| # 2: Calculation of Loan amount | ||||||||||
| Present Value of monthly payment | =pv(rate,nper,pmt,fv) | |||||||||
| $ 22,511.88 | ||||||||||
| Where, | ||||||||||
| rate | = | 0.003363 | ||||||||
| nper | = | 3*12 | = | 36 | ||||||
| pmt | = | $ -665 | ||||||||
| fv | = | 0 | ||||||||
| Note: | ||||||||||
| Loan amount is the present vaue of future payments. | ||||||||||
| (b) | Amount owed | $ 12,219.87 | ||||||||
| Working: | ||||||||||
| Loan value at the end of 17 months | ||||||||||
| Present Value of monthly payment | =pv(rate,nper,pmt,fv) | |||||||||
| $ 12,219.87 | ||||||||||
| Where, | ||||||||||
| rate | = | 0.003363 | ||||||||
| nper | = | 36-17 | = | 19 | ||||||
| pmt | = | $ -665 | ||||||||
| fv | = | 0 | ||||||||
| (c) | Principal repaid | $ 10,292.00 |
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