tricky question

anno38 · **Joined:** Sun, 9 Jan 2011 03:12:59 UTC **Posts:** 3

i need help with this question:

jane is 20 years old today. jane is going to put $1000 into her savings account on her 21th birthday and again on every birthday for 20 payments. she earn 5%, paid annually. how much money will be in the account after she collects her interest and makes her 20th payment?

this is my attempt:

i calculate the PV for 19 years first
pmt=1000, n=19, i=5, fv=0, pv=?

pv = 30539

then, calculate the principle 1000 x 19 = 19000
then take 30539- 19000= 11539 interest

so if jane collect interest 11539 on the 19 payment , the remaining in the account is 19000.

she again make last payment 1000 into account on her 40th birthday.
the account would left with 20,000

Am i doing this correct, can anyone give me some guidance.

greatly appreciate.

ann
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Denis · **Posted:** Sun, 16 Jan 2011 05:07:19 UTC

Ann, were you not given formulas by your teacher?
What you're doing is completely erroneous.

pmt = 1000 ; n = 20 ; i = .05 ; fv = ?
fv = 33,065.9541....

Or by formula:
fv = 1000(1.05^20 - 1) / .05 = 33,065.9541....

Monarchist · **Joined:** Mon, 28 Feb 2011 17:01:43 UTC **Posts:** 2

Denis is right. This is a trivial annuity-immediate question. You can google the concept "annuity-immediate." For example: http://en.wikipedia.org/wiki/Annuity_(finance_theory). The formula you need is $S=R\frac{(1+i)^{n}-1}{i}=1000\frac{1.05^{20}-1}{0.05}=33065.95$

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