Question
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?
Answers
GPT 3.5
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.
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.