Question

What rate of interest is required if $2,000 is deposited into an account, compounded monthly, so that you will have $3675.17 at the end of 10 years.

Answer 1

this is an algebra problem. Consider your base as 2000 + something = 3675.17 . Now you need to figure out what that something should be. Any ideas?

Answer 2

1675.17 would be that something. Is that what is plugged into the compound equation?

Answer 3

yes something = 3675.17, but you need to figure out what something actually is. It is a way to count the interest you need to make in order to get to 1675.17 in 10 years.

Answer 4

err 1675.17

Answer 5

So would you use A=P(1+r/n)^nt? I am confused what I would plug in for each variable.

Answer 6

Here is the compound interest formula: \[\Large A = P(1 + \frac{ r }{ n })^{nt}\]
A = Amount at maturity = $3675.17
P = Principal Amount = $2,000
r = Annual interest rate in decimal
n = compounding period (compounded how many times a year) = 12 (because it is compounded monthly)
t = years invested = 10

Find r.

Answer 7

Ahh, thank you so much! So the previously found 1675 number is irrelevant, correct? Also when I get to 1.83=(1+r/12)^120.. how do I bring down the exponent?

Answer 8

In these types of problems don't round the numbers early because it will affect the answer very much due to being raised to very high exponent such as 120.
So keep 3675.17 / 2000 as 1.837585
To bring down the exponent, take the 120th root on both sides:
(1.837585)^(1/120) = (1+r/12) Solve for r.

Answer 9

Taking the 120th root is same as saying raise both sides of the equation to the exponent 1/120.

Answer 10

R=0.3707. Would the A=Pert equation not work because it is not compounded continuously? Also, would the rate be 37.07%?

Answer 11

I am getting a different r value. You may want to check on the calculation again. I will answer the other parts after we get the correct r.

Answer 12

This time I got R=0.0609. Does that work?

Answer 13

Yes. That is the rate in decimal. And in percentage it is 6.099% or now you can round it to 6.1%

Answer 14

To verify, you can plug in the numbers on the right, including r = 0.061, into the right side of the equation and see if you get $3675.17.

Answer 15

You use A = Pe^(rt) only if it explicitly states the interest is compounded CONTINUOUSLY.
For all other compound interest calculations, use the above formula.
If it says the interest is compounded monthly then n = 12 (because that is how many times it is compounded in a year).
If interest is compounded semi-annually then n = 2
interest is compounded daily then n = 365

Answer 16

If interest is compounded quarterly, then n = 4

Answer 17

Yay I finally understand! Thank you so much, you are a fabulous person.

Answer 18

You are very welcome. Glad to be able to assist. :)