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Question

Part 1
A woman decides to invest ​$3000 in an IRA CD at the end of each year for 10 years. If she makes these payments and the certificates all pay 8​%, compounded​ annually, how much will she have at the end of the 10 ​years?
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Part 1
At the end of 10 ​years, the woman will have approximately ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answer 1

To calculate the future value of a series of cash flows (payments) made at the end of each year, we can use the formula for the future value of an ordinary annuity:

$$FV=P\times \frac{(1+r{)}^n-1}{r}$$

Where:

• $FV$ is the future value of the annuity.
• $P$ is the annual payment (in this case, $3000).
• $r$ is the annual interest rate (in this case, 8% or 0.08).
• $n$ is the number of payments (in this case, 10 years).

Substituting the values into the formula:

$$FV=3000\times \frac{(1+0.08{)}^{10}-1}{0.08}$$

First, calculate $(1+0.08{)}^{10}$:

$$(1.08{)}^{10}\approx 2.1589$$

Now plug this value back into the formula:

$$FV=3000\times \frac{2.1589-1}{0.08}$$ $$FV=3000\times \frac{1.1589}{0.08}$$ $$FV=3000\times 14.48625$$ $$FV\approx 43458.75$$

Thus, at the end of 10 years, the woman will have approximately $43,458.75.