Answer to Question #279034 in Financial Math for Ajay

Question

A mortgage of 665,000 is amortized over 25 years by makind end of month payments of 3560.

What is the annual rate of interest compounded semi annualy?

What is value of final payment?

What is the total interest cost for the debt over 25 years?

Answer 1

What is the annual rate of interest compounded semi annually?

Yearly payments;

=monthly payments $\times$ 12

$=3560\times12=42720$

annual rate of interest

$A=P[(1+r)^n-1]$

$42720=665000[(1+r)^n-1]$

$(1+r)^n=\frac{42720}{665000}+1$

$(1+r)^n=1.0642$

Since n=1

$r=1.064-1=0.064=6.4\%$

Therefore annual rate of interest compounded semi annually is;

$=\frac{r}{2}=\frac{6.4\%}{2}=3.2\%$

What is value of final payment?

=yearly payments$\times$ number of years

$=42720\times25$

$=1,068,000$

What is the total interest cost for the debt over 25 years?

Interest=$1,068,000-665000=403,000$ '

Interest rate=$\frac{403,000}{665000}=0.606=60.6\%$