Liz and Bob just had a baby named Isabelle, and they want to save enough money for Isabelle to go to college. Assume that they start making monthly payments when Isabelle is 5 into an ordinary annuity earning 4.1%, and they calculate that they will need $28,700.00 by the time Isabelle turns 18. How much should they deposit every month so that they reach their goal?
Deposit amount = $
Answer (2)
To determine how much Liz and Bob need to deposit each month into an ordinary annuity, we use the future value formula for an annuity:
F V = P × r ( 1 + r ) n − 1
Where:
F V is the future value of the annuity, which is $28,700.00 in this case.
P is the monthly deposit that we need to find.
r is the monthly interest rate.
n is the total number of payments.
Step-by-Step Calculation:
Determine the monthly interest rate :
The annual interest rate is 4.1%. Convert this to a monthly interest rate by dividing by 12:
r = 12 4.1% = 12 0.041 ≈ 0.0034167
Calculate the number of payments :
Since Isabelle will start college at 18 and the payments start when she is 5, there are 13 years of payments:
n = 13 × 12 = 156
Rearrange the formula to solve for P :
P = ( 1 + r ) n − 1 F V ⋅ r
Substitute the known values into the formula :
P = ( 1 + 0.0034167 ) 156 − 1 28 , 700 × 0.0034167
Calculate :
First, calculate the expression in the denominator:
( 1 + 0.0034167 ) 156
Calculate this value and then subtract 1.
Finally, compute P :
P comes out to approximately $146.14.
Therefore, Liz and Bob should deposit approximately $146.14 each month to reach their goal of $28,700 by the time Isabelle turns 18.
Liz and Bob should deposit approximately $138.88 each month to save $28,700 for Isabelle's college education. This calculation uses the future value formula for an ordinary annuity, considering an interest rate of 4.1%. The payments will begin when Isabelle turns 5 and will continue until she turns 18.
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