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Answer :
To determine how much Zeke needs to deposit now in order to have a balance of [tex]$50,000 in his savings account after 10 years with a simple interest rate of 3%, we can use the simple interest formula:
\[ A = P + P \cdot r \cdot t \]
Here:
- \( A \) is the future balance, which is $[/tex]50,000.
- [tex]\( r \)[/tex] is the interest rate as a decimal, so 3% becomes 0.03.
- [tex]\( t \)[/tex] is the time in years, which is 10 years.
- [tex]\( P \)[/tex] is the principal amount that Zeke needs to deposit now.
First, we rearrange the formula to solve for [tex]\( P \)[/tex]:
[tex]\[ A = P (1 + r \cdot t) \][/tex]
Now, solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{A}{1 + r \cdot t} \][/tex]
Substitute the known values into the formula:
[tex]\[ P = \frac{50000}{1 + 0.03 \times 10} \][/tex]
[tex]\[ P = \frac{50000}{1 + 0.3} \][/tex]
[tex]\[ P = \frac{50000}{1.3} \][/tex]
Calculating this gives:
[tex]\[ P \approx 38461.54 \][/tex]
Rounding this to the nearest dollar, Zeke will need to invest [tex]$38,462 now to achieve his goal.
So, Zeke needs to deposit $[/tex]38,462 in his savings account today to have $50,000 after 10 years with a simple interest rate of 3%.
\[ A = P + P \cdot r \cdot t \]
Here:
- \( A \) is the future balance, which is $[/tex]50,000.
- [tex]\( r \)[/tex] is the interest rate as a decimal, so 3% becomes 0.03.
- [tex]\( t \)[/tex] is the time in years, which is 10 years.
- [tex]\( P \)[/tex] is the principal amount that Zeke needs to deposit now.
First, we rearrange the formula to solve for [tex]\( P \)[/tex]:
[tex]\[ A = P (1 + r \cdot t) \][/tex]
Now, solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{A}{1 + r \cdot t} \][/tex]
Substitute the known values into the formula:
[tex]\[ P = \frac{50000}{1 + 0.03 \times 10} \][/tex]
[tex]\[ P = \frac{50000}{1 + 0.3} \][/tex]
[tex]\[ P = \frac{50000}{1.3} \][/tex]
Calculating this gives:
[tex]\[ P \approx 38461.54 \][/tex]
Rounding this to the nearest dollar, Zeke will need to invest [tex]$38,462 now to achieve his goal.
So, Zeke needs to deposit $[/tex]38,462 in his savings account today to have $50,000 after 10 years with a simple interest rate of 3%.
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