Compound Interest

ras-j wrote:Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?


A. $1500
B. $1750
C. $2000
D. $2500
E. $3000
If interest rate for 6 months will be 4% then how x is 2500?

Hi ras-j!

You can also solve this using the compound interest formula:


where:
A = Final Value
P = Initial Investment
r = interest rate (as a decimal)
n = # times compounded per year
t = # of years

Here the initial is unknown, so I'll call it X. Since we want to earn $100, that would be X+100. The rate is .08, the # of times is quarterly, so 4, and we have 6 months or 1/2 of a year.

A = 100+X
P = X
r = .08
n = 4
t = 1/2

plug this in and solve for X (and don't forget to approximate!!)

Now when I multiply 1.02 times 1.02, I actually get 1.0404, but I'm approximating, so I'm rounding to 1.04. That gives us:

100 + x = 1.04x
100 = 0.04x
10000 = 4x
x = 2500.

**NOTE: You can actually think of this formula a bit more simply. Notice that the compounding factor (the +.02) isn't the same as the annual rate. That is because we compound more than once a year. This is actually the same with your credit cards. If you have an annual rate of say 12% but it is compounded monthly. Then each month, you aren't charged 12% (that would end up being HUGE), you're only charged 12%/12 mos, so 1% each month.

So, that means that you can write the formula as

A = P (1+ rate at each compound) ^ (number of times I'll need to compound)

This might make it easier, since 8% compounded quarterly would be 2% each time, and I will only have 2 compounds in a 6 month period, I can immediately write:

A = P(1.02)^2

Hope this Helps!

Whit