Anna wants to invest her K3000 savings for three years. She has the choice of an account that pays 7.6% p.a. simple interest or another that pays 6.8% p.a., compounded quarterly. Calculate the interest earned in each case and decide which is the better financial option.
1. For the account with simple interest:
Interest earned = Principal x Rate x Time
= K3000 x 7.6% x 3 years
= K3000 x 0.076 x 3
= K684
2. For the account with compound interest:
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = amount after t years
P = principal amount (K3000)
r = annual interest rate (6.8% or 0.068)
n = number of times interest is compounded per year (quarterly, so n=4)
t = number of years (3)
A = K3000(1 + 0.068/4)^(4*3)
A = K3000(1 + 0.017)^12
A = K3000(1.017)^12
A = K3000(1.221)
A = K3663
Interest earned = A - P
Interest earned = K3663 - K3000
Interest earned = K663
Therefore, the interest earned in the first case (simple interest) is K684, and in the second case (compound interest) is K663. Based on these calculations, the better financial option would be the account with simple interest as it would earn Anna more interest over the three-year period.