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

Answer:

5.7% per year

Step-by-step explanation:

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

$A = R*(\frac{(1+\frac{r}{n})^{nt}-1 }{\frac{r}{n} } )$

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:

$155,514 = 675*(\frac{(1+\frac{r}{12} )^{156}-1}{\frac{r}{12} })$

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

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

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

Solving that in a graphic calculator,

r = 0.057

r = 5.7% per year