Final answer:
To calculate the future value for quarterly deposits in an account with a 20% annual interest rate compounded quarterly, we use the future value of an annuity formula. Each deposit grows according to that formula and the total in the account after 2 years and 3 months is the sum of the future values of each deposit.
Step-by-step explanation:
Calculating Future Value with Compound Interest
When calculating the future value for money deposited quarterly into an account with compound interest, we can use the future value of an annuity formula. For a regular deposit of $100 with an interest rate of 20% compounded quarterly for a period of 2 years and 3 months (which is 9 quarters), we construct a table to show the accumulation of each quarterly payment.
The future value (FV) formula for compound interest is FV = P × (1 + r/n)nt, where P is the principal amount, r is the annual nominal interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Quarterly Payments Table
- 1st quarter deposit at the end of the first quarter; FV = $100 × (1 + 0.20/4)1
- 2nd quarter deposit, FV = $100 × (1 + 0.20/4)2
- ... (repeat this process for each quarter)
- 9th quarter deposit (final deposit), FV = $100 × (1 + 0.20/4)9
The total money in the account at the end of the period is the sum of the future values of each deposit. We repeat the calculation for each deposit made at the end of each quarter, then add the results together to obtain the total amount.
The complete question is: K100 is deposited at the end of each quarter in an account that pays 20% compounded quarterly. How much money will we have in the account in 2 years and 3 months? Present the quarterly payments in a table is: