Question

Rockie needs $5,000 to pay for a certification program in 3 years. he can invest at an interest rate of 5.5%. how much money does he need to invest today to have a total of $5,000 in 3 years? A. $12.50

B. $31.44
C. $31.64
D. $100.00

Answer 1

Rockie needs to invest approximately $4263.91 today to have $5,000 in 3 years at an interest rate of 5.5%. The calculation involves using the present value formula for compound interest, which none of the provided choices match.

Step-by-step explanation:

The student's question is related to determining the present value of a future sum of money, which involves compound interest calculations. To find out how much Rockie needs to invest today to have $5,000 in 3 years at an interest rate of 5.5%, we can use the formula for the present value of a future sum:

PV = FV / (1 + r)^n

Where:
PV = present value (the amount to invest today)
FV = future value ($5,000)
r = annual interest rate (5.5%)
n = number of years (3)

We can calculate Rockie's present value as follows:

PV = $5,000 / (1 + 0.055)^3

Calculating the above expression:

PV = $5,000 / (1.055)^3
PV = $5,000 / 1.17276
PV ≈ $4263.91

Hence, Rockie needs to invest approximately $4263.91 today to have $5,000 in 3 years at an interest rate of 5.5%. None of the provided choices (A, B, C, D) are correct.