Answer:
Approximately $86,897.24
Step-by-step explanation:
To calculate the final amount in Jimmy's savings account at the end of 15 years, we need to consider the monthly deposits and the compound interest earned.
Let's break down the problem step by step:
1. Calculate the monthly interest rate:
Since the annual interest rate is 2.8% and it is compounded monthly, we need to calculate the monthly interest rate. We divide the annual interest rate by 12 (the number of months in a year):
Monthly interest rate = 2.8% / 12 = 0.028 / 12 = 0.0023333 (approximately)
2. Determine the total number of months:
Since we are considering a period of 15 years, and each year has 12 months, the total number of months is:
Total months = 15 years * 12 months/year = 180 months
3. Calculate the future value of monthly deposits and compound interest:
To calculate the future value, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value (final amount in the account)
P = Monthly deposit amount
r = Monthly interest rate
n = Total number of months
Let's substitute the values into the formula:
FV = 260 * [(1 + 0.0023333)^180 - 1] / 0.0023333
Calculating this expression will give us the final amount in Jimmy's savings account after 15 years.
Using a calculator or spreadsheet, the result is approximately $86,897.24.
Therefore, at the end of 15 years, the account will be worth approximately $86,897.24.
Answer:
$58,214.00
Step-by-step explanation:
To find the future value of the account where equal payments are made at the beginning of each period for a specified number of periods, with interest compounded at the end of each period, we can use the Future Value of an Annuity Due formula:
[tex]FV=\dfrac{PMT}{\frac{r}{n}}\left[\left(1+\dfrac{r}{n}\right)^{nt}-1\right]\left(1+\dfrac{r}{n}\right)[/tex]
where:
In this case:
Substitute the given values into the formula and solve for FV:
[tex]FV=\dfrac{260}{\frac{0.028}{12}}\left[\left(1+\dfrac{0.028}{12}\right)^{12 \cdot 15}-1\right]\left(1+\dfrac{0.028}{12}\right)[/tex]
[tex]FV=\dfrac{780000}{7}\left[\left(1.002333...\right)^{180}-1\right]\left(1.002333...\right)[/tex]
[tex]FV=58213.9971...[/tex]
[tex]FV=58214.00[/tex]
Therefore, the future value of the account rounded to the nearest cent is:
[tex]\Large\boxed{\boxed{\$58,214.00}}[/tex]
