Question

A retired Police officer invests K5000 in a credit union that pays an interest rate of 5% per annum, compounded quarterly. Exactly 2 years later she invests a further K6000 with the credit union under the same conditions. How much total interest will she have earned 5 years after the original investment?​

Answer 1

To solve this problem, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total amount, P is the principal (the initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

First, let's calculate the amount that the retired police officer would have after 2 years from her initial investment of K5000:

A₁ = P(1 + r/n)^(nt)
A₁ = 5000(1 + 0.05/4)^(4*2)
A₁ ≈ K5,563.06

Now let's find the amount that she would have 5 years after the initial investment, including the additional investment of K6000 made 2 years after the initial investment:

A₂ = P(1 + r/n)^(nt) + P₂(1 + r/n)^(nt)
A₂ = 5000(1 + 0.05/4)^(4*5) + 6000(1 + 0.05/4)^(4*3)
A₂ ≈ K13,221.35

To find the total interest earned, we need to subtract the total amount from the total principal invested:

Total interest = A₂ - (P + P₂)
Total interest = K13,221.35 - (K5000 + K6000)
Total interest ≈ K2,221.35

Therefore, the retired police officer would have earned approximately K2,221.35 in total interest 5 years after the original investment.