Question

11. Len invests $5200 at 3%/a simple interest, while his friend Dave invests $3600 at 5%/a simple interest. How long will it take for Dave’s investment to be worth more than Len’s?

Answer 1

I = Prt, right?

Answer 2

yes

Answer 3

can you show me how to fully evaluate this?

Answer 4

Unfortunately, this is only the interest calculation. What is an expression for the total value of the investment?

Hint: P + I

Answer 5

Substitute for I. What do you get?

Answer 6

sorry this is not for me i just need the solved question

Answer 7

Oh, well. It just doesn't work that way. It requires work from you. Sorry if that's an inconvenience.

Answer 8

im confused on how to approach this question

Answer 9

Answer my questions and you will be unconfused.

I = Prt is the formulae for calculating interest only.
P + I is an expression for the total value of the investment.

P + Prt is an equivalent expression using algebraic substitution.

P(1 + rt) is another expression for the same thing.

Now what?

Answer 10

you substitute the principal and the interest in the last equation

Answer 11

Now we build. We need an expression for the value of Len's investment at any time in the future. Just substitute known values:


P(1 + rt) ==? $5200(1 + 0.03t)

You write an expression for the value of Dave's investment at any time.

Answer 12

$3600(1+0.05t)

Answer 13

Perfect. Now, we need just one theoretical idea before we finish. We need to decide whose investment is growing faster. Hopefully, it is obvious that Dave's investment will be growing faster since 5200*0.03 = 156 and 3600*0.05 = 180. Make sense?

Answer 14

yes

Answer 15

I lied. We need one more idea.

Since we have established that Dave's investment is growing faster then :Len's, if we can find a moment when they are exactly equal, then we can be assured that Dave will be ahead at any time after that moment. Do you agree with this premise?