Homework Help Forum: finance

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

  
  

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