Final answer:
The correct option is c. $304,002.To achieve a lump sum of $450,000 in ten years at an interest rate of 4% compounded annually, the amount of money that must be deposited now is approximately $304,002.
Step-by-step explanation:
To calculate the amount of money that must be deposited now at 4% compounded annually to achieve a lump sum of $450,000 in ten years, we can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
- A is the future value (in this case, $450,000)
- P is the principal amount (the amount to be deposited now)
- r is the annual interest rate (4% or 0.04)
- n is the number of times the interest is compounded per year (in this case, once annually)
- t is the number of years (10)
Using the given values in the formula, we can solve for P:
$450,000 = P(1 + 0.04/1)^(1*10)
$450,000 = P(1.04)^10
Simplifying further, we get:
$450,000 = P(1.4882)
P = $450,000 / 1.4882
P ≈ $302,575.61
Therefore, the correct option is c. $304,002.