Answer:
Ms P's monthly payment would be approximately $72,876.37.
Explanation:
To calculate Ms P's monthly payment, we can use the formula for the future value of an ordinary annuity:
\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]
where:
FV = Future Value (desired amount at retirement, which is 8 million in this case)
P = Monthly Payment
r = Monthly Interest Rate (annual interest rate divided by 12)
n = Number of compounding periods (total number of months she contributes to the fund)
Given:
Future Value (FV) = 8,000,000
Annual Interest Rate = 17.5% p.a
Monthly Interest Rate (r) = 17.5% / 12 = 0.175 / 12 = 0.01458333333 (approximately)
Number of compounding periods (n) = 55 (from her 25th birthday to her 55th birthday, a total of 55 years)
Now, let's calculate her monthly payment (P):
\[ P = \frac{FV \times r}{(1 + r)^n - 1} \]
\[ P = \frac{8,000,000 \times 0.01458333333}{(1 + 0.01458333333)^{55} - 1} \]
Calculate the numerator:
\[ P = \frac{116,666.66664}{(1.01458333333)^{55} - 1} \]
Calculate the denominator:
\[ P = \frac{116,666.66664}{2.6010115817 - 1} \]
\[ P = \frac{116,666.66664}{1.6010115817} \]
\[ P \approx 72,876.37 \]
Ms P's monthly payment would be approximately $72,876.37.