Question

You plan to make two deposits to your bank account - one deposit today for $X and one deposit in four years for $3X. You would like to withdraw $20,000 from this bank account in 6 years, and another $10,000 in 12 years. You can earn an effective rate of 5% per year. What is $X?

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?

Answer 1

You plan to make two deposits to your bank account - one deposit today for $X and one deposit in four years for $3X. You would like to withdraw $20,000 from this bank account in 6 years, and another $10,000 in 12 years. You can earn an effective rate of 5% per year. What is $X?

Present value of withdrawals = present value of deposits

Present value of withdrawals is:

Particulars	First withdraw	Second	Total
Amount withdrawal	$          20,000	$          10,000
× present value factor	0.746215	0.556837
Present value	$    14,924.31	$       5,568.37	$ 20,492.68

First deposit today and another deposit in four years.

Present value factor for today is 1 and for four years is 0.783526

Present value of deposits = $20,492.68

X + 0.783526 × 3X = $20,492.68

X = $20,492.68/ 3.468107 = $5,908.89

Deposit today is $5,908.89

Deposit in four years = 3 × $5,908.89= $17,726.68

Second question:

Particulars	Year 10	Year 11	Year 12	Year 13	Total
Amount of fee	$    50,000.00	$    52,500.00	$ 55,125.00	$ 57,881.25
× present value factor	0.613913	0.584679	0.556837	0.530321
Present value	$    30,695.66	$    30,695.66	$ 30,695.66	$ 30,695.66	$ 122,782.65

Total amount required today is $122,782.65

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