Question

2. You want to have enough money in the bank to pay for your daughter’s education when the time comes. You expect to make 4 annual payments for college, with the first payment in 10 years. The first payment will be for $50,000 and each subsequent payment will be 5% higher than the previous payment. If you expect to earn 5% a year on your deposits, how much do you need in the bank now to ensure you will have the desired amount to fund your daughter’s education? (8 points)

Answer 1

Solution :-

1st Year Fees = $50,000

2nd Year Fees = $50,000 * ( 1 + 0.05 ) = $52,500

3rd Year Fees = $52,500 * ( 1 + 0.05 ) = $55,125

4th Year Fees = $55,125 * ( 1 + 0.05 ) = $57,881.25

Now the Present value of Fees at Discount Rate = 5%

= [ $50,000 / (1+0.05)¹⁰ ] + [ $52,500 / (1+0.05)¹¹ ] + [ $55,125 / (1+0.05)¹² ] + [ $57,881.25 / (1+0.05)¹³ ]

= [ $50,000 / (1+0.05)¹⁰ ] + [ $52,500 / (1+0.05)¹¹ ] + [ $55,125 / (1+0.05)¹² ] + [ $57,881.25 / (1+0.05)¹³ ]

= [ $55,000 * 0.614 ] + [ $52,500 * 0.585 ] + [ $55,125 * 0.557 ] + [ $57,881.25 * 0.5303 ]

= $30,695.66 + $30,695.66 + $30,695.66 + $30,695.66

= $122,782.65

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