You invest money at a certain annual interest rate p. Interrest is paid once a year. Use r as the percentage..

Question

when r is = p/100.
Every year you multiply your current capital by a factor of________?(where your answer depends on r)
In 2 years you will multiply your initial capital with ________?
in 3 years?
In t years?

Answer 1

What you're looking for is the very basics of compound interest.

What's going on with p and r in these questions is that p is usually expressed as a percentage (e.g., 5%). Now 5% really means 0.05, but if you think of p as being 5, then you have to divide it by 100 to get the interest rate as a number rather than as a percent: p/100 = 5/100 = 0.05, so we'll say that r = 0.05. (I guess "r" stands for "rate." But usually you use the symbol "i" for interest rate.)

So, for the first blank:
Q: By what factor does your capital increase in the course of a year? (That's what they're really asking.)
A: Well, you get to keep your original capital, so you have to multiply by 1. And you also get an amount of interest equal to 0.05 times the capital you started with. So you need to multiply by (1 plus 0.05), or 1.05.

The second year, your total capital (initial capital x 1.05) increases by a factor of 1.05 again. So "In 2 years you will multiply your initial capital" by 1.05 x 1.05 = 1.05^2.

And in three years you need to multiply by 1.05^3, and in t years you multiply by 1.05^t.

Make sense?
I hope so. As I said, this is the basis for everything in compound interest theory. It's basically simple (as above), but the problems and concepts can get very complex.
Good luck.

Answer 2

B_0 = initial investment
B(t)=B_0(1+p/100)^t,
so everyyear you multiply your current capital by a factor of
(1+p/100)=(1+r)
in two year you multiply your initial capital by:
(1+p/100)^2=(1+r)^2
in three years by
(1+p/100)^3=(1+r)^3
as I wrote before in t years by:
(1+p/100)^t