Final answer:
Luis Litt's identical deposits to purchase a $300,000 watch in 6 years, calculated with a 9% annual simple interest rate, can be found by solving the equation that equates the future value of three deposits made at different times to the total desired amount.
Step-by-step explanation:
Luis Litt wants to figure out how large three identical deposits should be in order to buy a $300,000 watch in 6 years with an interest rate of 9% per annum on simple interest. To determine this, we calculate the future value of each deposit and ensure their sum equals to $300,000 in 6 years. Given that the deposits are made at year 0, 2, and 4, we can calculate the future value of these deposits separately and then equate their total to $300,000.
The formula for future value using simple interest is: FV = P + (P × r × t), where P is the principal, r is the annual interest rate, and t is the time in years. Using this formula:
- Deposit made today (year 0) will accumulate interest for 6 years.
- Deposit made in 2 years (year 2) will accumulate interest for 4 years.
- Deposit made in 4 years (year 4) will accumulate interest for 2 years.
Let's denote each deposit as 'D'. Then:
Future value of the first deposit after 6 years: D + (D × 0.09 × 6)
Future value of the second deposit after 4 years: D + (D × 0.09 × 4)
Future value of the third deposit after 2 years: D + (D × 0.09 × 2)
Adding the future values of all three deposits, we get:
3D + (D × 0.09 × 6) + (D × 0.09 × 4) + (D × 0.09 × 2) = $300,000
Now, we can solve for 'D' to find the size of each deposit. The final calculation involves taking the sum of D's future values and equating it to $300,000 followed by solving for 'D'.