Use TVM Solver on your calculator to answer the following questions. Round each answer to
the nearest cent.
You deposit each month into an account earning interest compounded monthly.
a) How much will you have in the account in 15 years?
b) How much total money will you put into the account?
$

Question

Use TVM Solver on your calculator to answer the following questions. Round each answer to
the nearest cent.
You deposit

each month into an account earning

interest compounded monthly.
a) How much will you have in the account in 15 years?
b) How much total money will you put into the account?
$

UpStudy AI · Accepted Answer

**Step 1. Determine the parameters.**  
- Monthly deposit (payment): $$ PMT = \$300 $$  
- Annual interest rate: $$ 2\% $$  
- Monthly interest rate:  
  $$
  i = \frac{2\%}{12} = \frac{0.02}{12} \approx 0.00166667
  $$  
- Total number of deposits over 15 years:  
  $$
  n = 15 \times 12 = 180 \text{ months}
  $$

**Step 2. Calculate the future value of the annuity.**

The formula for the future value of an annuity is:  
$$
FV = PMT \times \frac{(1+i)^n - 1}{i}
$$

Substitute the given values:  
$$
FV = 300 \times \frac{(1+0.00166667)^{180} - 1}{0.00166667}
$$

First, calculate $$(1+i)^n$$:  
$$
(1+0.00166667)^{180} \approx 1.34986
$$

Then, compute the numerator:  
$$
(1.34986 - 1) \approx 0.34986
$$

Divide by $$ i $$:  
$$
\frac{0.34986}{0.00166667} \approx 209.916
$$

Multiply by $$ PMT = 300$$:  
$$
FV \approx 300 \times 209.916 \approx 62\,974.80
$$

Rounded to the nearest cent, the future value is:  
$$
FV \approx \$62\,974.80
$$

**Step 3. Calculate the total amount deposited.**  
The total deposits over 15 years are calculated as:  
$$
\text{Total Deposits} = PMT \times n = 300 \times 180 = \$54\,000
$$

**Final Answers:**  
a) The account will have approximately $$ \$62\,974.80 $$ after 15 years.  
b) You will have deposited a total of $$ \$54\,000 $$.
a) After 15 years, you will have approximately \$62,974.80 in the account. b) You will have deposited a total of \$54,000 into the account.

Use TVM Solver on your calculator to answer the following questions. Round each answer to
the nearest cent.
You deposit each month into an account earning interest compounded monthly.
a) How much will you have in the account in 15 years?
b) How much total money will you put into the account?
$

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Use TVM Solver on your calculator to answer the following questions. Round each answer to the nearest cent. You deposit each month into an account earning interest compounded monthly. a) How much will you have in the account in 15 years? b) How much total money will you put into the account? $

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Use TVM Solver on your calculator to answer the following questions. Round each answer to
the nearest cent.
You deposit each month into an account earning interest compounded monthly.
a) How much will you have in the account in 15 years?
b) How much total money will you put into the account?
$