Answer:
Explanation:
Your sister can use the formula for calculating the present value of an annuity to determine how much she can withdraw each year.
The formula for the present value of an annuity is:
PV = Payment x (1 - (1 + r)^-n) / r
Where:
- PV is the present value of the annuity
- Payment is the amount of each withdrawal
- r is the annual interest rate
- n is the number of periods (in this case, 25 years)
We can rearrange this formula to solve for Payment:
Payment = PV x r / (1 - (1 + r)^-n)
We know that your sister has R375 000 to start with, and she wants to end up with zero in 25 years. So, her present value (PV) is R375 000, and we can assume her future value (FV) is zero.
Using the future value formula, we can calculate the interest rate she needs to earn in order to end up with zero in 25 years:
FV = PV x (1 + r)^n
0 = 375000 x (1 + r)^25
(1 + r)^25 = 1
1 + r = (1)^1/25
r = 0
This means that your sister needs to withdraw all of her money over the 25 years in order to end up with zero at the end.
Her withdrawal each year would be:
Payment = PV x r / (1 - (1 + r)^-n)
Payment = 375000 x 0.08 / (1 - (1 + 0.08)^-25)
Payment = R34,028.82 per year
Your sister can withdraw R34,028.82 at the beginning of each year for the next 25 years, and she will end up with zero at the end, assuming she earns an 8% return on her invested funds.