Monday

March 30, 2015

March 30, 2015

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

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 4:02pmFor 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 - How much money should be invested today in order to have $100,000 in an ...

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% ...

math - a company will need $30.000 in 7 years for a new addition. To meat this ...

Pre Calc - $1 is invested into an account that has a APR of 8% compounded ...

math - Suppose 48,000 is invested at an interest rate of 4.2%, compounded ...

Finance - Joe and Sue invested $1500 at Bank America in 2000, at 4% compounded ...

Math 111 - Suppose that $5000 is invested in an account with an account with an ...