Question

Aunt Mabel promised to give you $9000 when you successfully complete your freshman year, $6000 when you successfully complete your sophomore year, $1000 when you successfully complete your junior year, and $8000 when you successfully complete your senior year. Aunt Mabel made this promise when you graduated from High School and let's assume you go directly to the University of Illinois and graduate in four years. Aunt Mabel expects the interest rates to be 5.250% during your freshman year, 2.500% during your sophomore year, 3.250% during your junior year, and 9.250% during your senior year. If Aunt Mable can predict interest rates accurately, she will deposit into her bank account $____________. (dollars, rounded to two places after the decimal)

Answer 1

Solution :

At every stage the formula used will be :

$\frac{\text{available balance}}{(1+\text{interest rate})}= \text{required bank balance}$

After the junior year, Aunt Mabel's bank balance will be :

$=\frac{8000}{1.0925}$

= $ 7,322.65

Aunt Mabel's bank balance after sophomore year will be :

7,322.65 + 1000 = $ 8,322.65

$=\frac{8,322.65}{1.0325}$

= $ 8060.677

After the freshman year, bank balance of Aunt Mable's will be :

8060.677 + 6000 = $ 14,060.677

$=\frac{14,060.677}{1.0250}$

= $ 14.0606

If Aunt Mabel can predict the interest rate with accuracy, she will have to deposit :

$ 14.0606 + $ 9000 = $ 9,014.06

$=\frac{9014.06}{1.0525}$

= $ 8,565.241