Sally has a sum of $17000 that she invests at 5% compounded monthly. What equal monthly payments can she receive over a period of
a) 9 years?
Answer = $
b) 11 years?
Answer = $
Answer (1)
To solve this problem, we need to understand the concept of annuity payments, where an amount is invested, and equal periodic payouts are made over a specified period. Sally has $17000 invested at an annual interest rate of 5%, compounded monthly.
The formula to find the monthly payment (A) in an annuity is given by:
A = P × ( 1 + r ) n − 1 r ( 1 + r ) n
where:
P is the principal amount ($17000).
r is the monthly interest rate (annual rate divided by 12 months). In this case, 5% ÷ 12 = 0.4167% or 0.004167 .
n is the total number of payments (months).
a) For 9 years:
First, calculate n , the total number of monthly payments: 9 × 12 = 108 m o n t h s .
Substitute P = 17000 , r = 0.004167 , and n = 108 into the formula:
A = 17000 × ( 1 + 0.004167 ) 108 − 1 0.004167 ( 1 + 0.004167 ) 108
After solving using a calculator:
A ≈ 191.79
So, Sally can receive approximately $191.79 per month for 9 years.
b) For 11 years:
Calculate n , the total number of monthly payments: 11 × 12 = 132 m o n t h s .
Substitute P = 17000 , r = 0.004167 , and n = 132 into the formula:
A = 17000 × ( 1 + 0.004167 ) 132 − 1 0.004167 ( 1 + 0.004167 ) 132
After solving using a calculator:
A ≈ 167.70
So, Sally can receive approximately $167.70 per month for 11 years.
Thus, the equal monthly payments Sally can receive depend on the number of years she plans to withdraw from her investment.
