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**Dharshi****Member**- Registered: 2006-10-31
- Posts: 56

How much will you have accumulated over a period of 20 years if, in an IRA which has a 10% interest rate compounded monthly, you annually invest:

a. $1

b. $100

c. $20,000

d. Part (a) is called the effective yield of an account. How could Part (a) be used to determine Parts (b) and (c)?\

We need to use the compound interest formula.Anyone can help me with that?

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

The formula for the amount (A) accumulated over a period of N months on a principle P invested at R% compound interest compounded monthly is..

A=P(1+R)[sup]N[/sup]

Just plugin the values and find A.

Note that R here is to be taken as 0.1 or 1/10 and that N will be in months i.e. 20×12 months!

*Last edited by ZHero (2010-06-30 06:15:18)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

I don't think this is a straight compound interest. You can use CI when a fixed sum is invested but Dharshi says there's an annual investment. So new money has to be added each year in addition to the interest.

Before I work out a revised formula let's just check I've got it right:

(i) each year $1 is invested

(ii) for 20 years

(iii) interest rate is compound (ie. add the calculated interest to the investment for the next year)

(iv) 10% per month ! This seems a bit generous! Did you mean an equivalent annual rate of 10% but calculated monthly?

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**soroban****Member**- Registered: 2007-03-09
- Posts: 452

. . . . . . . um, not quite

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

"annual rate = 10% monthly rate = 10%/12"

Don't think so.

monthly multiplier = (1.10)^(1/12) = m (say) [ so that 12 monthly multpliers give the yearly multiplier]

then monthly rate = (m-1) x 100 % [ to convert back to percentage ]

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you!

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