Final answer:
To calculate the final value of an investment with initial 5-year monthly contributions followed by 14 years of growth without additional contributions, use the future value of an annuity formula for the first phase, followed by the future value of a lump sum formula for the second phase.
Step-by-step explanation:
To calculate the future value of an investment with monthly contributions at an interest rate compounded monthly, followed by a period of growth without additional contributions, we divide our approach into two phases: the accumulation phase and the growth phase.
Accumulation Phase
During the first 5 years, you save $140 monthly at a 5.9% annual interest rate, compounded monthly.
The formula for future value of an annuity compounded monthly is:
FV = P × { [ (1 + r/n)^(nt) - 1 ] / (r/n) }
Where:
P = monthly payment
r = annual interest rate
n = number of times interest is compounded per year
t = number of years
Plugging the values in, we get:
FV = 140 × { [ (1 + 0.059/12)^(12×5) - 1 ] / (0.059/12) }
Growth Phase: No Contributions
After 5 years, no more contributions are made and the investment continues to grow for the next 14 years.
The formula for the future value of a lump sum is:
FV = PV × (1 + r/n)^(nt)
Where:
PV = present value (value after 5 years)
We calculate the new future value using the amount from the accumulation phase as PV, and t = 14 years.