Explanation:
To calculate how much should be placed in an account now to have $21,200 cash for a new car 7 years from now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = future value (amount of money after t years)
P = present value (amount of money now)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, we have:
A = $21,200
r = 0.064 (6.4% as a decimal)
t = 7
n = 1 (the interest is compounded annually)
So, we can solve for P:
P = A / (1 + r/n)^(nt)
P = $21,200 / (1 + 0.064)^(7)
P = $15,093.35
Therefore, the person should place $15,093.35 in an account now to have $21,200 cash for a new car 7 years from now, at an annual interest rate of 6.4%.