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What amount of money must be deposited now at 4%, compounded annually, to achieve a lump sum of $450,000 in ten (10) years?

a. $205,376
b. $208,436
c. $304,002
d. $369,158

1 Answer

3 votes

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.

User Pierre Michard
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