Susie has decided to make deposits at the end of each quarter in the amout of $5,000. After three years, she makes more deposits and just lets the money sit there for two more years. What will be the balance in the account at the end of that time? Assume the bank will give her 8% interest compounded quarterly.
To find the balance in the account at the end of the given time period, we can break down the problem into two parts:
1. Calculating the future value of the deposits made during the first three years.
2. Calculating the future value of the deposits made during the last two years.
First, let's calculate the future value of the deposits made during the first three years. Each deposit of $5,000 is made at the end of each quarter, which means there will be a total of 4 deposits per year.
Since the interest is compounded quarterly at a rate of 8%, we can use the formula for compound interest:
Future Value = P * (1 + r/n)^(n*t)
Where:
- P is the principal amount (initial deposit),
- r is the annual interest rate (8%),
- n is the number of times interest is compounded per year (4, since it's compounded quarterly), and
- t is the number of years.
For each deposit, the principal amount (P) will be $5,000. So, the future value of the deposits made during the first three years can be calculated as:
Future Value of Deposits = $5,000 * (1 + 0.08/4)^(4*3)
Now, let's calculate the future value of the deposits made during the last two years. Since Susie is not making any additional deposits and is letting the money sit, we only need to calculate the interest generated during this period.
Using the same formula, with the changes for the number of years, we can calculate the future value:
Future Value of Interest = Future Value of Deposits * (1 + 0.08/4)^(4*2)
Finally, to find the balance in the account at the end of the given time period, we add the future value of the deposits to the future value of the interest:
Balance = Future Value of Deposits + Future Value of Interest
Plugging in the values into the equation will give you the balance in the account at the end of the time period.