Question

A loan of $27,150.00 at 5.00% compounded semi-annually is to be repaid with payments at the end of every 6 months. The loan was settled in 4 years.

a. Calculate the size of the periodic payment.

$3,406.15

$4,200.70

$3,786.54

$4,276.00

b. Calculate the total interest paid.

$3,142.32

$30,292.32

-$644.22

$6,928.86

Answer 1

Given: Principal = 27,150.

Interest = 5% compounded semi annually.

Payment- At the end of every 6 months

Question 1: Calculate the Periodic payments

Periodic Payment = P × r × (1 + r)^n / ((1 + r)^n - 1), where P= Present Value of the Amount, r= interest rate, n=tenure.
Periodic Payment = (27,150 x (0.05/2) x (1+0.05/2)^8) / ((1+.05/2)^8 - 1)

Therefore, the periodic Payment = $ 3,786.54

Note: This can also be solved using the PMT function of Excel

The PMT function uses the following arguments:

1. Rate – The interest rate of the loan (as Interest is compounded semi annually, we are dividing the Rate by 2)
2. Nper – Total number of payments for the loan taken (As the payments are made semi annually, multiply the total years by 2 to arrive at tenure)
3. Pv – The present value or total amount that a series of future payments is worth now. It is also termed as the principal of a loan.
4. Fv – The future value of a loan is 0

Question 2: Calculate the total Interest Paid:

Solution:  We solved from the previous option that every instalment is equal to 3,786.54 and it will be paid every 6 months till the end of 4th year.

Total Instalments Paid = $ 3,786.54 x 8 = $ 30,292.31

Now these total Installments paid include the Principal as well as the Interest Amount.

So, $ 30,292.31 = 27,150 + Interest

Interest = 30,292.31 - 27,150 = $ 3,142.32 (Oprtion a)

Read more at:
https://economictimes.indiatimes.com/analysis/what-is-emi-and-how-is-it-calculated/articleshow/39880530.cms?utm_source=contentofinterest&utm_medium=text&utm_campaign=cppst

ffective Annual Rate = (1+(r/n))ⁿ − 1

= (1 + (.05/2))^2 - 1

= 5.06%

Now, That we have the Effective annual interest Rate, lets look at the options:

a. Calculate the size of the periodic payment.

b. Calculate the total interest paid.

$3,142.32

$30,292.32

-$644.22

$6,928.86