word problem

[sud21]

Someone invested a certain amount of money at the 2.5 percent annual interest rate. At the end of the fifth year, the total amount in the account is $11250. How much did he invest?

[Anurag@Gurome]

Someone invested a certain amount of money at the 2.5 percent annual interest rate. At the end of the fifth year, the total amount in the account is $11250. How much did he invest?

Let us assume the initial investment was $P.

Now, assuming the interest is simple,
P*(1 + (5*2.5)/100) = 11250 ---> P = 11250/1.125 = 10,000

[Brent@GMATPrepNow]

Someone invested a certain amount of money at the 2.5 percent annual interest rate. At the end of the fifth year, the total amount in the account is $11250. How much did he invest?

Are we talking simple interest or compound interest here?

If it's simple interest, let P = the initial investment.
With simple interest, the interest for each year is the same: 0.025P
So, in 5 years, the total interest = 0.025P + 0.025P + 0.025P + 0.025P + 0.025P = 0.125P
When we add this interest to the initial investment, P, we get a total value of 1.125P
If the total value = 11,250 then we must solve the following equation for P: 1.125P = 11,250
So, P = 10,000


If it's compound interest, and IF the interest is compounded once per year, then after 5 years the total value of the investment = P(1.025)^5
If the total value = 11,250 then we must solve the following equation for P: P(1.025)^5 = 11,250

To solve this one, we need to use logarithms (AND a calculator)

Cheers,
Brent