Answer:
To find the monthly deposit required to reach $104,000 in 14 years with an annuity paying 5.7% interest compounded monthly, the future value annuity formula is used, adjusting for the specific values given. By solving this equation for P, the monthly payment, the exact deposit amount will be determined.
Step-by-step explanation:
The student's question revolves around the concept of annuities, specifically finding the monthly deposit required to achieve a future sum with a given interest rate and compound frequency. To solve this, we will use the future value annuity formula for compounding monthly:
Future Value Annuity Formula: FV = P * [((1 + r/n)^(nt) - 1) / (r/n)]
Where:
FV is the future value of the annuity, which is $104,000.
P is the monthly payment.
r is the annual interest rate (5.7% or 0.057 as a decimal).
n is the number of times that interest is compounded per year (12 for monthly).
t is the number of years (14 in this scenario).
Plugging in the values we get:
104,000 = P * [((1 + 0.057/12)^(12*14) - 1) / (0.057/12)]
Calculating the right-hand side of the equation will give us the monthly deposit P. Solving for P, the student can determine the amount of money to be deposited every month to reach their goal of $104,000 in 14 years with an annuity paying 5.7% interest compounded monthly.