Question

Suppose $20,000 is invested into an account where interest is compounded semiannually. After 30 years the balance is
$41,951.
What was the interest rate as a percent?
Round the answer to the nearest hundredth of a percent.

Answer 1

Compound Interest Formula: $A=P(1+\frac{r}{n})^{nt}$

P = initial investment of 20,000

r = interest rate (What we need to find)

n=number of compounding periods per year (Semiannually means twice per year)

A= Amount after t-years

Okay, let's plug it all in.

41,951 = 20000 (1 + r/2)^2(30)  

41,951/20000  = (1 + r/2)^60  

(41,951/20000 )^1/60 = 1 + r/2  

(41,951/20000 )^1/60 - 1 = r/2  

2( (41,951/20000 )^1/60 - 1 ) = r  

0.02484539... = r

0.02484 * 100 = 2.48% rounded to the nearest hundredth of a percent

I hope I've helped! :)