Posted by **tiff** on Sunday, October 25, 2009 at 1:58pm.

Today, Mark invested $5,000 into an account that guarantees 7.50% p.a., compounded monthly and Madonna invested $5,000 into account guaranteeing 8.125% p.a., compounded quarterly.

How long will it take (in years) for the value of Madonna's investment to be three times as much as Mark's?

- finance -
**MathMate**, Sunday, October 25, 2009 at 4:02pm
For mark:

interest rate

= 7.5% p.a.

= 7.5%/12 per period of one month

= .625%

Future value of $5000 in n years, FVK(n)

= 5000*(1.00625)^{12*n}

For Madonna,

interest rate

= 8.125% p.a.

= 8.125%/4 per quarter

= 2.03125% per quarter

Future value of $5000 in n years, FVD(n)

= 5000*(1.0203125)^{4*n}

We look for n where

FVD(n) = 3FVK(n)

5000*(1.0203125)^{4*n}

= 3*5000*(1.00625)^{12*n}

(1.0203125)^{4*n} / (1.00625)^{12*n} = 3

Take log on both sides

4*n*log(1.0203125)-12*n*log(1.00625) = 3

n = log(3)/(4log(1.0203125-12log(1.00625))

= 193.785 years

Check:

in 193.785 years,

Mark will have $9,801,861,882.04

Madonna will have $29,405,482,100.99

## Answer This Question

## Related Questions

- finance - Today, Mark invested $5,000 into an account that guarantees 7.50% p.a...
- algebra - $7,000 is invested into two accounts: 4,000 into an account paying 5% ...
- MATH HELP - Ben Garrison invested $15,000 at 5% compounded daily in a credit ...
- MATH - Ben Garrison invested $15,000 at 5% compounded daily in a credit union ...
- College Algebra - Investment A: $5,000 invested for 7 years compounded ...
- UOG - An initial investment of $12,000 is invested for 2 years in an account ...
- Finance - 3. Joe and Sue invested $2000 at Bank America in 1995, at 6% ...
- Algebra ASAP - Suppose that $17,000 is invested in a savings account paying 5.1...
- Finance - Joe and Sue invested $1500 at Bank America in 2000, at 4% compounded ...
- math - You invest $1,000 at 4% compounded daily. Two years later you take the ...

More Related Questions