Question

Your friend deposits $2,500 into a savings account for 4 years. The account pays 10.2% p.a compounding quarterly. The equivalent simple interest rate expressed on a per annum basis is

Answer 1

Solution:

The formula we use to calculate compound interest is given by:
A = P*(1 + r/n)^(nt)

A = Future value of the investment/loan, including interest
P = Principal investment amount (it is the initial deposit or loan amount)
r = Annual interest rate
n = It is the number of times that interest is compounded per year
t = The number of years the money is invested or borrowed.

The formula for total compounded interest is given by P*(1 + r/n)^(nt)- P (it means total amount minus principal amount).

In the given question n=4 (compounded quarterly so annually 4 quarters)
P=$2500
t=4 years
r=10.2/100=.102

Total interest amount= [2500*(1+.102/4)^4*4]-2500
=[2500*(1+.0255)^16]-2500
=2500*(1.0255)^16-2500
=2500*1.496134-2500
=3740.335-2500
=1240.335 =$1240.34 (approximately)

To find the equivalent simple interest rate, we will equate the interest amount that we get above to interest amount from simple interest. The formula to calculate simple interest amount on a per annum basis is given by:
Interest amount =P*r*t/100
P = Principal investment amount (it is the initial deposit or loan amount)
r = Annual interest rate
t = The number of years the money is invested or borrowed.

Here, P=$2500, t=4 years and r=?

S0, 1240.34= 2500*r*4/100
r=(1240.34*100)/(2500*4)
r=12.4% (approximately)

Thus, the equivalent per annum simple interest rate is 12.4% approximately.