At the end of each month of next year we plan to lnvest K200 into an account that bears interest 8% p.a. compounded monthly. After this time our payment will reduce to K125 per month. What will be the value of our investment after three years?

Answer 1

To calculate the value of the investment after three years, we first need to calculate the future value of the monthly investments for the first year, then the future value of the reduced monthly investments for the next two years.

1. Future value of monthly investments after one year:
Using the formula for compound interest:
FV = P * (1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (K200)
r = annual interest rate (8% or 0.08)
n = number of times interest is compounded per year (12 for monthly)
t = time in years (1)

FV = K200 * (1 + 0.08/12)^(12*1)
FV = K200 * (1 + 0.00667)^12
FV = K200 * (1.00667)^12
FV = K200 * 1.0833
FV = K216.66

2. Calculate the future value of reduced monthly investments for the next two years:
We need to calculate the future value of K125 per month for two years at an interest rate of 8% compounded monthly.

P = K125
r = 0.08
n = 12
t = 2

FV = K125 * ((1 + 0.08/12)^(12*2) - 1) / (0.08/12)
FV = K125 * ((1.00667)^24 - 1) / 0.00667
FV = K125 * (1.1834 - 1) / 0.00667
FV = K125 * 0.1834 / 0.00667
FV = K3458.76

3. Calculate the total value of the investment after three years:
Total Value = Future value of monthly investments after one year + Future value of reduced monthly investments for the next two years
Total Value = K216.66 + K3458.76
Total Value = K3675.42

Therefore, the value of the investment after three years will be K3675.42.