Question

At the end of six years your savings

account has a balance of $1,236.34. Your
original deposit was $1000 and it was
compounded semi-annually. What was
the interest rate for this particular
account?

Answer 1

3.567%

Explanation:

There are formulas for all of the variables in a loan amortization except the interest rate. That must be found using a financial calculator, spreadsheet formula, or iterative procedures. Here, we found the value using a graphing calculator.

The interest rate was 3.567% per year.

_____

Additional comment

That interest rate gives a 6th-year balance of $1236.31. The rate is closer to ...

3.5674%

The formula for the balance is ...

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

where principal P is earning interest at rate r compounded n times per year for t years.

The graph shows the value of r (in percent) that makes this difference zero:

f(r) = 1236.34 -1000(1 +r/2)^(2·6)