To determine how much Tom needs to deposit now to reach his goal of $50,000 in five years with an interest rate of 4% compounded annually, we can use the formula for the present value (PV) of a future amount (FV):
\[ PV = \frac{FV}{(1 + r)^n} \]
where:
- \(FV\) is the future value ($50,000),
- \(r\) is the interest rate (0.04),
- \(n\) is the number of years (5).
Plugging in the values:
\[ PV = \frac{50000}{(1 + 0.04)^5} \]
Calculating \((1 + 0.04)^5\):
\[ (1.04)^5 \approx 1.21665 \]
Now substitute back into the present value formula:
\[ PV = \frac{50000}{1.21665} \approx 41,050.12 \]
This means Tom should deposit approximately $41,050.12 now.
Looking at the options provided:
A. $40,000
B. $42,000
C. $45,000
D. $47,000
The closest option is B. $42,000.
1 answer