Question

What was the annual interest rate if a CD earned $161.46 on a principal of $2,500 over 25 months?

Answer 1

We will find the interest rate by using the following expression:

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

Here A is the amount, P is the principal, r is the rate, n is the number of interest is compounded per unit t, and t is the time.

Now, we replace the values and solve for r:

`2661.46=2500(1+(r)/(25))^(25)\Rightarrow(2661.46)/(2500)=(1+(r)/(12))^{12\cdot(25)/(144)}`
`\Rightarrow\ln ((2661.46)/(2500))=(25)/(12)\text{ln}(1+(r)/(12))\Rightarrow0.062541\approx(25)/(12)\ln ((x)/(12)+1)\Rightarrow0.0300404\approx\ln ((x)/(12)+1)`
`\Rightarrow(x)/(12)+1\approx1.0305\Rightarrow(x)/(12)\approx0.03404961\Rightarrow x\approx0.3215954`

So, the annual interest rate was approximately 6.3%.