Rita puts $10,000 into each of two different assets. The first asset pays 10 percent interest and the second pays 5 percent. According to the rule of 70, what is the approximate difference in the value of the two assets after 14 years?

Question

a.

$20,000
b.

$12,000
c.

$14,000
d.

$15,500

Answer 1

The Rule of 70 is a way to estimate the number of years it takes for an investment to double in value by dividing 70 by the annual interest rate.

1. For the first asset (10% interest): \[ \text{Doubling Time} = \frac{70}{10} = 7 \text{ years} \] After 14 years (which is 2 doubling periods), the amount will double twice: \[ \text{Value} = 10,000 \times 2 \times 2 = 40,000 \]

2. For the second asset (5% interest): \[ \text{Doubling Time} = \frac{70}{5} = 14 \text{ years} \] After 14 years, the amount will double once: \[ \text{Value} = 10,000 \times 2 = 20,000 \]

3. Calculating the difference: \[ \text{Difference in Value} = \text{Value of First Asset} - \text{Value of Second Asset} = 40,000 - 20,000 = 20,000 \]

Thus, the approximate difference in the value of the two assets after 14 years is:

a. $20,000