Final answer:
To reach $1,750 billion in 10 years with a 6% interest rate compounded quarterly, approximately $954.88 billion must be invested today.
Step-by-step explanation:
To calculate the amount of money that needs to be invested today to reach a future value, we can use the formula for compound interest:
A = P(1 + r/n)nt
Where:
- A is the future value
- P is the principal amount (the amount to be invested today)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, we are given that the future value (A) is $1,750 billion, the interest rate (r) is 6%, and the interest is compounded quarterly, so the number of times the interest is compounded per year (n) is 4.
Plugging in these values into the formula:
$1,750 billion = P(1 + 0.06/4)(4)(10)
Simplifying:
$1,750 billion = P(1.015)40
Dividing both sides by (1.015)40:
$1,750 billion / (1.015)40 = P
Using a calculator, we can evaluate (1.015)40 to be approximately 1.833, so:
$1,750 billion / 1.833 = P
Simplifying:
P ≈ $954.88 billion
Therefore, approximately $954.88 billion must be invested today to reach $1,750 billion in 10 years.