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

Answer:

Following are the solution to the given point:

Explanation:

Calculating the value of the effective interest rate:

Formula:

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

                                  $=\frac{12}{2} \\\\ =6\%$

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:

$= 5000 \times (\frac{F}{P}, 6\% ,9) \times (\frac{A}{P}, 6\%,4)\\\\= 5000 \times 1.689479 \times 0.288591\\\\= 2437.85$

Calculating the value of the total interest paid:

$= 2437.85 \times 4 - 5000\\\\= 9751.40-5000\\\\ = 4751.40$