Question

Find the payment necessary to amortize a 6.3% loan of 7500 compounded semiannually, with 6 semiannual payments. Find the payment necessary to amortize the loan and the total payments and the total amount of interest paid based on calculated semiannual payments.

Answer 1

Semiannual payment = $ 1391.37

Total payment = $ 8348.22

Interest paid = $ 848.22

Explanation:

Since, the semiannual payment formula of a loan,

`P=(PV((r)/(2)))/(1-(1+(r)/(2))^(-n))`

Where,

PV = present value of the loan,

n = number of semiannual payments,

r = annual rate,

Here, PV = 7500, r = 6.3% =0.063, n = 6,

By substituting the value,

The semiannual payment would be,

`P=(7500((0.063)/(2)))/(1-(1+(0.063)/(2))^(-6))`

`\approx \$ 1391.37`

Also, total payment = semiannual payment × total semiannual periods

= 1391.37 × 6

= $ 8348.22,

Also, the interest paid = total payment - present value

= 8348.22 - 7500

= $ 848.22