Question

Starting next year you will need $10000 annually for 4 years to complete your education (one year from today you will withdraw the first $100000. yur uncle deposits an amount today in a bank paying 5% annual interest which will provide the needed $10000 payments. a how large must the deposit be? b. how much will be in the account immediately after you make the first withdrawal?

Answer 1

The deposit needs to be $39,255.25 and the amount in the account immediately after the first withdrawal is $29,255.25.

Step-by-step explanation:

To calculate the size of the deposit needed, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of years. Plugging in the values, we have:

FV = $10,000 * ((1 + 0.05)^4 - 1) / 0.05 = $39,255.25

So, the deposit needs to be $39,255.25.

To find the amount in the account immediately after the first withdrawal, we can subtract the first $10,000 payment from the future value:

$39,255.25 - $10,000 = $29,255.25