Person X invests R 150 at the end of each month with bank X who adds interest at 6% per annum, compounded monthly. Person Y invests R 380 at the end of each year with bank Y who adds interest at 9% per annum compounded annually. Who will have the most money available after exactly 17 years?

Answer 1

To find out who will have the most money available after 17 years, we need to calculate the future value of the investments for both Person X and Person Y.

For Person X:
The monthly investment is R 150, and the annual interest rate is 6% compounded monthly.
The number of compounding periods is 17 years * 12 months = 204 months.
The formula for calculating the future value of an investment with compound interest is:

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

where:
FV = Future Value
P = Principal amount (the monthly investment)
r = Annual interest rate (6%)
n = Number of compounding periods per year (12 for monthly compounding)
t = Number of years (17)

Plugging in the values:

FV = 150(1 + 0.06/12)^(12*17)
FV = R 150(1 + 0.005)^(204)
FV = R 150(1.005)^(204)

FV ≈ R 150(2.051899)
FV ≈ R 307.7849

For Person Y:
The yearly investment is R 380, and the annual interest rate is 9% compounded annually.
The number of compounding periods is 17 years.

Using the same formula as above:

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

FV = 380(1 + 0.09/1)^(1*17)
FV = R 380(1.09)^17
FV = R 380(3.464898)
FV = R 1,319.66284

After 17 years, Person Y will have the most money available with R 1,319.66284 compared to Person X with R 307.7849.