Finance. A person wishes to have 24800 cash for a new car 4 years from now. How much should be placed in an account now, if the account pays 6.6% annual interest rate, compounded weekly?
To determine how much should be placed in the account now to have $24,800 in 4 years, we can use the formula for compound interest.
The formula for compound interest is:
A = P*(1+r/n)^(n*t)
Where:
A = the future value of the investment ($24,800 in this case),
P = the principal amount (the amount to be placed in the account now),
r = the annual interest rate as a decimal (6.6% = 0.066 in this case),
n = the number of times interest is compounded per year (52 weeks in this case, for weekly compounding),
t = the number of years (4 years in this case).
Now, we can substitute the given values into the formula and solve for P:
$24,800 = P*(1+0.066/52)^(52*4)
Simplifying the equation:
$24,800 = P*(1.001269)^208
Now, divide both sides of the equation by (1.001269)^208:
P = $24,800 / (1.001269)^208
We can solve this equation using a financial calculator, spreadsheet software, or an online compound interest calculator. Entering the values, we find:
P ≈ $21,085.51
Therefore, approximately $21,085.51 should be placed in the account now to have $24,800 in 4 years, with a 6.6% annual interest rate compounded weekly.