Shakira has accumulated R 250 000 to supplement her pension. She is ready to retire and wants to know how much money she can take out at the end of each month for the fund to last 15 years assuming a 6% interest rate, compounded monthly?
To calculate how much money Shakira can take out at the end of each month for 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = amount of money accumulated after t years
P = principal amount (initial investment) = R 250 000
r = annual interest rate = 6% = 0.06
n = number of times interest is compounded per year = 12 (monthly)
t = number of years = 15
Plugging in the values, we get:
A = R 250 000 (1 + 0.06/12)^(12*15)
A = R 250 000 (1 + 0.005)^(180)
A = R 250 000 (1.005)^180
A = R 250 000 (2.013563)
A = R 503 390.75
Now, we can calculate the monthly payment using the present value of an annuity formula:
Pmt = A / (((1 + r/n)^(nt) - 1) / (r/n))
Plugging in the values, we get:
Pmt = R 503 390.75 / (((1 + 0.06/12)^(12*15) - 1) / (0.06/12))
Pmt = R 503 390.75 / (((1.005)^180 - 1) / 0.005)
Pmt = R 503 390.75 / ((2.013563 - 1) / 0.005)
Pmt = R 503 390.75 / (1.013563 / 0.005)
Pmt = R 503 390.75 / 0.202713
Pmt = R 2 483.58
Therefore, Shakira can take out approximately R 2 483.58 at the end of each month for the fund to last 15 years assuming a 6% interest rate, compounded monthly.