Six annual payments of $250 into savings account earns 1.5% annually. What is the value of the account at the end of the six years?
Rate
Periods
Payment
Future value
To find the future value of the savings account at the end of six years, we can use the formula for compound interest:
Future Value = Payment * [(1 + Rate)^Periods - 1] / Rate
In this case:
- Rate = 1.5% = 0.015 (convert percentage to decimal)
- Periods = 6 (number of years)
- Payment = $250 (amount deposited annually)
Substituting these values into the formula:
Future Value = $250 * [(1 + 0.015)^6 - 1] / 0.015
Now, let's calculate it step by step:
1. First, let's calculate the value inside the bracket:
(1 + 0.015)^6 = 1.093139542 (using a calculator or a spreadsheet)
[(1 + 0.015)^6 - 1] = 0.093139542
2. Next, divide the value inside the bracket by the interest rate:
0.093139542 / 0.015 = 6.209317614
3. Finally, multiply the payment by the result from step 2 to get the future value:
$250 * 6.209317614 = $1552.3294035
Therefore, the value of the account at the end of the six years is approximately $1,552.33.