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4. How much should a father deposit in his savings account so that he, will be able 5 d its to withdraw \( \$ 100,000 \) after 3 years if the bank's interest rate is \( 3 \% \) ?

Ask by Johnston Brewer. in the Philippines
Dec 09,2024

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Tutor-Verified Answer

Answer

The father should deposit approximately $91,574.55 to withdraw $100,000 after 3 years at a 3% interest rate.

Solution

To determine how much a father should deposit in his savings account to withdraw $100,000 after 3 years at an interest rate of 3%, we can use the formula for the future value of a single sum: \[ FV = PV \times (1 + r)^n \] Where: - \( FV \) is the future value (the amount he wants to withdraw, which is $100,000), - \( PV \) is the present value (the amount he needs to deposit now), - \( r \) is the interest rate (3% or 0.03), - \( n \) is the number of years (3 years). We need to rearrange the formula to solve for \( PV \): \[ PV = \frac{FV}{(1 + r)^n} \] Now, substituting the values into the formula: \[ PV = \frac{100,000}{(1 + 0.03)^3} \] Calculating \( (1 + 0.03)^3 \): \[ (1 + 0.03)^3 = (1.03)^3 \approx 1.092727 \] Now, substituting this back into the equation for \( PV \): \[ PV = \frac{100,000}{1.092727} \approx 91,574.55 \] Therefore, the father should deposit approximately **$91,574.55** in his savings account to be able to withdraw $100,000 after 3 years at an interest rate of 3%.

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Bonus Knowledge

To figure out how much a father needs to deposit today to accumulate \( \$100,000 \) in 3 years with a \( 3\% \) interest rate, you can use the formula for present value: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( FV \) is the future value (\$100,000), - \( r \) is the interest rate (0.03), and - \( n \) is the number of years (3). Plugging in the numbers: \[ PV = \frac{100,000}{(1 + 0.03)^3} \approx \frac{100,000}{1.092727} \approx 91,574.69 \] So, the father should deposit approximately \( \$91,574.69 \) today! Did you know that Albert Einstein once called compound interest the "eighth wonder of the world"? He apparently believed it was more powerful than any other force in economics! This principle applies perfectly here. Your father’s money doesn’t just sit there – it grows, thanks to interest compounding over time! For anyone looking to make the most out of savings, setting clear financial goals is key. In this case, calculating the present value can prevent common pitfalls, like underestimating the amount needed. Also, always shop around for bank accounts with competitive interest rates. Even a small difference can lead to more substantial savings in the long haul!

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