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March 14th, 2014, 10:06 AM   #1
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Financial Mathematics (Need Verification)

(1)
A couple has two children of ages five and eight years old. They decide to deposit a sum of money into the children's banks accounts.

For the first child, $5000 and $10000 are deposited when the child reaches the age of 10 and 16 years respectively. The annual interest rate is 5% durings the saving period. Calculate the accrued amount obtained by the child at the age of 21 years.

However, the couple makes a single deposit for the second child when the child is 12 years old. The annual interest rate is 4% compounded semi-annually. Determine the amount that needs to be deposited so that the second child, at the age of 21 years, obtain an accrued amount that equal to that of their first child.

[color=#0000FF]For the first child, A = 5000(1.05)^11 + 10000(1.05)^5 = $21314.51
For the second child, A = P[(1 + (0.04/2)]^(2*9) => P = 21314.51 / [(1.02)^18] = $14923.55[/color]

(2)
An employee deposits $10000 in a savings account at the end of the year. He deposits the same amount at the end of each year for the next 9 years. Subsequently, he deposits $15000 at the end of each year for next 20 years. The interest rate remains at 5% per annum during this period of 30 years. Calculate the present value of his savings for the
(a) first 10 years
(b) whole period of 30 years

[color=#0000FF](a) P = 10000[(1 - (1.05)^-10) / 0.05] = $77217.35
(b) P = 77217.35 + 15000[(1 - (1.05)^-20) / 0.05] = 77217.35+186933.16 = $264150.51[/color]

Another employee deposits a fixed amount at the end of each year for the same period of 30 years. Calculate the fixed amount deposited each year such that they both have the same amount of savings at the end of 30 years.

[color=#0000FF]R = 264150.51(0.05) / 1 - (1.05)^-30 = $17183.37[/color]
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March 15th, 2014, 11:56 AM   #2
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Re: Financial Mathematics (Need Verification)

1st part is correct.
Quote:
Originally Posted by ystiang
An employee deposits $10000 in a savings account at the end of the year. He deposits the same amount at the end of each year for the next 9 years. Subsequently, he deposits $15000 at the end of each year for next 20 years. The interest rate remains at 5% per annum during this period of 30 years. Calculate the present value of his savings for the
(a) first 10 years
(b) whole period of 30 years
[color=#0000FF](a) P = 10000[(1 - (1.05)^-10) / 0.05] = $77217.35
(b) P = 77217.35 + 15000[(1 - (1.05)^-20) / 0.05] = 77217.35+186933.16 = $264150.51[/color]
No. You certainly can't deposit $10,000 10 times and be left with only ~$77,000 !
Formula is:
10000[(1+.05)^10 - 1] / .05
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