To determine how much Miranda needs to put in the bank now, we need to calculate the present value of the future amount she wants to give her daughter. Here's a step-by-step explanation:
1. Identify the given values:
- Future value [tex]\( FV \)[/tex] which she wants to give her daughter: \[tex]$20,000
- Annual interest rate \( i \): 10% (which is 0.10 in decimal form)
- Time period \( t \): Miranda's daughter is currently 14 years old, and she wants to give her the money when she turns 18, which is in \( 18 - 14 = 4 \) years.
2. Present Value Formula:
\[ PV = \frac{FV}{(1 + i)^t} \]
Where:
- \( PV \) is the present value (the amount she needs to put in the bank now),
- \( FV \) is the future value (\$[/tex]20,000),
- [tex]\( i \)[/tex] is the annual interest rate (0.10),
- [tex]\( t \)[/tex] is the number of years (4).
3. Substitute the given values into the formula:
[tex]\[ PV = \frac{20000}{(1 + 0.10)^4} \][/tex]
4. Calculate the present value:
After performing the calculations, we find:
[tex]\[ PV = 13660.27 \][/tex]
Therefore, Miranda needs to put approximately \[tex]$13,660.27 in the bank now.
The correct answer is:
B. \$[/tex]13,660.27
