Question

To save for​ retirement, Karla Harby put ​$675675 each month into an ordinary annuity for 1313 years. Interest was compounded monthly. At the end of the 1313 ​years, the annuity was worth ​$155 comma 514155,514. What annual interest rate did she​ receive?

Answer 1

5.7% per year

Explanation:

For an ordinary annuity, the final amount can be calculated by:

`A = R*(((1+(r)/(n))^(nt)-1 )/((r)/(n) ) )`

Where A is the final amount, R is the value invested monthly, r is the annual interest, n is the number of months in a year, and t the time in years. So:

`155,514 = 675*(((1+(r)/(12) )^(156)-1)/((r)/(12) ))`

(\frac{(1+\frac{r}{12} )^{156}-1}{\frac{r}{12} }) = 230.39

`(((1+(r)/(12) )^(156)-1)/(r)) = 230.39/12`

(\frac{(1+\frac{r}{12} )^{156}-1}{r}) = 19.2

Solving that in a graphic calculator,

r = 0.057

r = 5.7% per year