SOLUTION: To save for retirement karla harby put $650 each month into an ordinary annuity for 14 years. Interest was compounded monthly. At the end of the 14 years, the annuity was worth $15

Question 1096881: To save for retirement karla harby put $650 each month into an ordinary annuity for 14 years. Interest was compounded monthly. At the end of the 14 years, the annuity was worth $154,986. What annual interest rate did she receive?
Please answer with Full Details.
Thank you
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

The formula for the value P of an annuity with regular deposits of amount A, n times per year for t years, at an annual interest rate of r, is

In your problem, we know A is 650, n is 12, and t is 14; we need to find r. The formula is

If you know the interest rate r and 3 of the other 4 numbers, you can calculate the missing number using the formula, or some form of it. But the interest rate r occurs in two different places in the formula, making it impossible to do a direct calculation to find the interest rate, if it is the unknown in the problem.

So all you can do is use some mathematical tool, like a graphing calculator, to find the answer. I used my TI-84 calculator to graph the two functions
and
and used the intersection of the two graphs to find the monthly interest rate is 0.00398 = 0.398%, making the annual interest rate 0.04776 = 4.776%.
RELATED QUESTIONS
To save for retirement, Karla Harby put $550 each month into an ordinary annuity for 14... (answered by robertb)

To save for retirement, Karla Harby put $500 each month into an ordinary annuity... (answered by CPhill,ikleyn)

To save for retirement, Karla Harby put $550 each month into an ordinary... (answered by Theo)

Eugene began to save for his retirement at age 20, and for 10 years he put $ 550 per... (answered by ikleyn)

Eugene began to save for his retirement at age 29, and for 11 years he put $ 500 per... (answered by ikleyn)

To save for the replacement of a computer, a business deposits $250 at the end of each... (answered by Solver92311,ikleyn)

Evelyn starts a retirement fund 10 years before retirement. She pays $100 per month into... (answered by ikleyn)

Suppose you put $ 525 a month for retirement into an annuity earning 7% compounded... (answered by ikleyn)

Wilma wants to withdraw $500 every month for three years. What amount must be deposited... (answered by josgarithmetic)