Jimbo invested $9,250 in an account that pays 6 percent simple interest (annually). How much more could he have earned over a 7-year period if the interest had compounded semi-annually

860.25

Explanation:

Solution

Simple interest = 9250 + (9250*0.06*7) = 13,135

Semi Annual Compound interest=A (1+r) ^nt) / n

9250 (1+0.06) ^7*2) / 2

=9250 (1+0.03) ^14

=9250 (1.03) ^14

=9250 (1.513) = 13,995.25

Take the difference between between simple and compound interest

13,995.25-13,135=860.25

The difference is that the interest in Option 2 gets capitalized faster.

Explanation:

Giving the following information:

Option 1:

$9,250 in an account that pays 6 percent simple interest (annually).

Option 2:

$9,250 n an account that pays 6 percent semiannually.

Number of years = 7 years

We need to use the following formula:

FV = PV * (1+i) ^n

Option 1:

FV = 9,250 * (1.06^7) = $13,908.58

Option 2:

FV = 9,250 * (1.03^14) = $13,991.45

n = 2*7 = 14

i = 0.06/2 = 0.03

The difference is that the interest in Option 2 gets capitalized faster.