Question

The International Monetary Fund is trying to raise $1,750 billion in 10 years for new funds to lend to developing countries. At 6% interest compounded quarterly, how much must it invest today to reach $1,750 billion in 10 years?

Answer 1

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.