Suppose $80,000 is invested into an account where interest is compounded annually. After 30 years the balance is $299,625. What was the interest rate as a percent?

Answer 1

Algebraically, the equation to solve should be 299625 = 80000 x (1+r%)^30.

299625/80000 = (1+0.01r)^30.

If you cannot use a calculator/excel to solve this, you can use log books.

Log(299625/80000)=30 × log (1+0.01r)

Log(3.74)= 30×log(1+0.01r)

0.5734/30=log(1+0.01r)

0.019=log(1+0.01r)

Taking antilog on both sides,

Antilog(0.019)=1+0.01r

1.045=1+0.01r

0.045=0.01r

r=4.5.

Alternatively, if you can use calculator, you can use exponential and ln functions.

If you can you excel, you can solve with goal seek or solver.