Question

You are taking a $5000 loan. You will pay it back in four equal amounts, paid every 6 months starting 5 years from now. The interest rate is 12% compounded semiannually. Calculate: The effective interest rate The amount of each semiannual payment The total interest paid

Answer 1

Following are the solution to the given point:

Step-by-step explanation:

Calculating the value of the effective interest rate:

Formula:

`\text{Effective interest rate} =\frac{\text{annual nominal rate of interest}}{\text{compound year}}`

`=(12)/(2) \\\\ =6\%`

Calculating the value of Effective annual rate of interest:

`=(1+ \text{The effective rate})^{\text{(compound number )}} -1`

`=(1+0.06)^2 -1\\\\=(1.06)^2 -1\\\\=1.1236-1\\\\=0.1236\\\\=12.36 \%`

Calculating the Amount in each semiannual payment:

`= 5000 * ((F)/(P), 6\% ,9) * ((A)/(P), 6\%,4)\\\\= 5000 * 1.689479 * 0.288591\\\\= 2437.85`

Calculating the value of the total interest paid:

`= 2437.85 * 4 - 5000\\\\= 9751.40-5000\\\\ = 4751.40`