Inez wants to have $14,750 in 5 years. Use the present value formula to calculate how much Inez should invest now at 4% interest, compounded quarterly in order to reach her goal.
(a) $11,800.00
(b) $12,080.30
(c) $12,088.28
(d) $12,123.42
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The present value formula is given by:
PV = FV / (1 + r/n)^(n*t)
Where:
- PV is the present value (the amount Inez needs to invest now)
- FV is the future value (the amount Inez wants to have in 5 years)
- r is the interest rate per period (4% or 0.04)
- n is the number of compounding periods per year (quarterly, so 4)
- t is the number of years
Plugging in the values:
PV = 14750 / (1 + 0.04 / 4)^(4*5)
PV = 14750 / (1 + 0.01)^(20)
PV = 14750 / (1.01)^20
PV ≈ 14750 / 1.2217
PV ≈ 12088.28
Therefore, Inez should invest approximately $12,088.28 now.
The correct answer is (c) $12,088.28.
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