How much will $850 amount to be in three years if it is invested at 8% interest compounded quarterly for 3 years

Question

A.) $886.47

B.) $952.43

C.) $1078.01 

D.) $1168.15

Answer 1

There are great formulas and calculators to do this for you, but let's break it down a little.

 

8% interest compounded quarterly means that you will compound 2% per quarter, which is four times a year. Do you see where I got that number? Four times a year means I have to divide my rate by 4. Sometimes you'll see this as r/n, where r is the interest rate and n is the number of times it is compounded annually.

 

So, after one quarter, the amount of interest accrued will be $850×2% or 850×0.02=17. Now I just add that to my original amount, so 850+17=867.

 

Of course, I could do all that in one step by finding 102% instead of 2%, which has the effect of adding in how much I started with. That means the simpler step is 850×1.02=867

 

So after one quarter, I'm left with 850×1.02=867

After another quarter, I'm left with 867×1.02=884.34

After yet another quarter, 884.34×1.02

 

This is really just repeated multiplication. Another way to write the amount after two quarters would be:

850×1.02×1.02

And after three quarters, we could write this as:

850×1.02×1.02×1.02

 

Thankfully, math has a method for organizing repeated multiplication so that you don't have to multiply this in your calculator dozens of times. Using exponents, we can rewrite 1.02×1.02 as 1.02²

That means that after two quarters, we will have 850×1.02²

After three quarters, we're left with 850×1.02³

Do you see the pattern?

 

Now, how many quarters are in three years?

If there are n quarters, we will be left with 850×1.02ⁿ

 

By the way, the general formula is A=P(1+r/n)^nt 

 

Answer 2

C

 

you have Principal=P=$850

rate=r=8%=8/100=0.08

n=number of times compounded=quaterly=4

t=time=3 years

 

formula

A=P(1+r/n)^nt

A=850(1+0.08/4)^4*3

850(1+0.02)^12

850(1.02)^12

850(1.2682417)

$1,078.0055 =$1,078.01