Question

If$2500was invested 6 years ago, andtheinterestwascompoundedquar-terly,whatwastheinterestrateifthecurrentvalueis$3425?

Answer 1

The interest rate for an investment of $2500 that grew to $3425 in 6 years with quarterly compounding is approximately 4.55%.

Step-by-step explanation:

To determine the interest rate of the compounded investment, we can use the formula for compound interest which is A = P(1 + r/n)^(nt), where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for in years.

Given that the initial investment (P) is $2500, the current value (A) is $3425, the interest is compounded quarterly (n = 4), and the time period (t) is 6 years, we can set up the equation as follows:

3425 = 2500(1 + r/4)^(4*6)

Dividing both sides by 2500 gives us:

1.37 = (1 + r/4)^(24)

We then take the 24th root of both sides to solve for (1 + r/4):

(1 + r/4) = 1.37^(1/24)

To find r, we subtract 1 from both sides and then multiply by 4:

r = [1.37^(1/24) - 1] * 4

Using a calculator, we find that r = 0.0455 or 4.55%

Therefore, the quarterly compounded interest rate that led to a current value of $3425 from a $2500 investment 6 years ago is approximately 4.55%.

Answer 2

The interest rate was 5.24%.

Step-by-step explanation:

You can use the following formula to calculate the interest rate:

i=n*((A/P)^1/nt-1), where:

i= interest rate

n= number of times interest is compounded= 4

A=value of investment= 3425

P= principal= 2500

t=time= 6

Now, you can replace the values on the formula:

i=4*((3425/2500)^1/4*6-1)

i=4*(1.37^1/24-1)

i=4*0.0131

i=0.0524

According to this, the answer is that the interest rate was 5.24%.