Sally has a sum of $23000 that she invests at 4% compounded monthly. What equal monthly payments can she receive over a period of:
a) 5 Years
b) 8 years
To find out the equal monthly payments Sally can receive, we can use the withdrawal formula for investments compounded monthly:
Withdrawal = P * (r * (1 + r)^n) / ((1 + r)^N - 1)
Where P is the principal amount ($23,000), r is the monthly interest rate (4%/12 = 0.333..%/month = 0.003333..), n is the number of payments, and N is the total number of payments.
a) 5 Years:
Number of payments for 5 years (monthly) = 5 x 12 = 60
Withdrawal = 23,000 * (0.003333.. * (1 + 0.003333..)^60) / ((1 + 0.003333..)^60 - 1)
Withdrawal ≈ $529.55
b) 8 Years:
Number of payments for 8 years (monthly) = 8 x 12 = 96
Withdrawal = 23,000 * (0.003333.. * (1 + 0.003333..)^96) / ((1 + 0.003333..)^96 - 1)
Withdrawal ≈ $363.69
So, Sally can receive equal monthly payments of approximately $529.55 over 5 years or $363.69 over 8 years.