Amount saving problem

Nick G

2008-06-17 6:44 am

Suppose you wish to save $20,000 by making a series of equal monthly deposits at the
end of each month for a period of 5 years. If the interest rate is 5% p.a. compounded
monthly how much should each monthly deposit be?

suppose the principal amount is P
P(1+0.05/12)60=20000
P=15584.10781
P/60=259.735
The desposit will be 260.

Is this right??

回答 (1)

[匿名]

2008-06-17 7:48 am

✔ 最佳答案

This is a problem of ordinary annuity (also referred as annuity-immediate).
It refers to the payments (e.g. R) are made at the end of each period (e.g.
a month)

Define:
S = the future value of an annuity.
R = the periodic payment in an annuity (the amortized payment).
i = interest rate per period
n = the number of periods

According to your question,
S = $20,000
i = 5% / 12 = 0.004167
n = 5 * 12 = 60

S = future value of 1st payment + future value of 2nd payment + future value of 3rd payment + .. + future value of 60th payment

$20,000 = R (1+i)^59 + R (1+i)^58 + R (1+i)^57 + ... + R
$20,000 = R ( (1+i)^60 - 1 ) / i (where i = 0.004167)
R = $20,000 / 60.00608 = $294.0913

Therefore, the monthly deposit is $294.0913

參考: You may find more information about annuity via http://en.wikipedia.org/wiki/Annuity_%28finance_theory%29

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