Mathematics: You put $125.32 at the end of each month in an investment plan that pays 2.5% interest, compounded monthly. how much will you have after 23 years? round to the nearest cent. a. $46,683.28 b. $4,564,471.88 c. $2,949.39 d. $3,832.84

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You put $125.32 at the end of each month in an - id125324040577, NaVaThEBeAsT

Ответ:

bultron1966

14.06.2020

Mathematics

The correct option is Option A $\boxed{{\mathbf{\$ 46,683}}{\mathbf{.28}}}$ .

Further explanation:

The future value of an annuity is the total worth of annuity payments at a particular point in the future.

The formula for future value of annuity is as follows,

$A=PMT\times\frac{{{{\left( {1 +\frac{r}{n}}\right)}^{nt - 1}}}}{{\frac{r}{n}}}$

Here, is the future value of annuity, PMT is the value of each annuity payment, is the interest rate and is the time in years.

If interest is compounded yearly then n=1 , if compounded semiannually then n=4 , if compounded quarterly then n=4 , if compounded month then n=12 .

Given:

It is given that the person invests $\$ 125.32$ at the end of each month with $2.5\%$ interest.

Step by step explanation:

Step 1:

The value of each annuity payment is $\$ 125.32$ , the interest rate is $2.5\%$ compounded monthly and time is $23{\text{ years}}$ .

The interest rate is compounded monthly therefore the value of is 12.

Step 2:

Now the future value of annuity can be calculated as,

$\begin{gathered}A=PMT\times\frac{{{{\left({1+\frac{r}{n}}\right)}^{nt-1}}}}{{\frac{r}{n}}}\hfill\\A=125.32\times\frac{{{{\left({1+\frac{{2.5\% }}{{12}}}\right)}^{12\times23-1}}}}{{\frac{{2.5\% }}{{12}}}}\hfill\\A=125.32\times\frac{{{{\left({1+\frac{{0.025}}{{12}}}\right)}^{275}}}}{{\frac{{0.025}}{{12}}}}\hfill\\A=46,683.28\hfill\\\end{gathered}$

Thus, the option A $\$46,683.28$ is correct.

Learn more:

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Future value of annuity

Keywords: Interest rate, future value, annuity, payment, compounded monthly, month, investment plan, invests, person, worth, particular point.

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You put $125.32 at the end of each month in an investment plan that pays 2.5% interest, compounded monthly. how much will you have after 23 years? round to the nearest cent.
a. $46,683.28
b. $4,564,471.88
c. $2,949.39
d. $3,832.84

Ответ:

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