Final answer:
To have $26,800 in 3 years with a 6.9% annual interest rate compounded weekly, one can calculate the present value by rearranging the compound interest formula. With the future value (A) known, and values for the rate (r), number of periods (n), and time (t), the initial deposit (P) can be found through the formula P = A / (1 + r/n)^(nt).
Step-by-step explanation:
To determine how much should be placed in an account now to have $26,800 for a new car in 3 years at a 6.9% annual interest rate, compounded weekly, we use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount (the initial deposit)
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per year
- t is the number of years the money is invested or borrowed for
In this case, A is $26,800, r is 0.069 (6.9% expressed as a decimal), n is 52 (since interest is compounded weekly), and t is 3.
To solve for P (the principal), we can rearrange the formula:
P = A / (1 + r/n)^(nt)
Plugging in our values:
P = $26,800 / (1 + 0.069/52)^(52*3)
After calculating the above expression, we can find the amount needed to deposit now.