You are given a choice of taking the simple interest on $100,000 invested for 2 years at a rate of 5%

Question

6) You are given a choice of taking the simple interest on $100,000 invested for 2 years at a rate of 5%

or the interest on 100,000 invested for 2 years at an interest rate 5% compound monthly

.

Which investment earns the greater amount of interest? Give the difference between the amounts of interest earned by the two investments.

The investment with ? is it COMPOUND OR SIMPLE interest earns $ ? MORE INTEREST▼

compound

simple

interest earns

$nothing

more in interest.

(Round to the nearest cent as needed.)

Answer 1

The formula for simple interest is I = Prt, where I = interest earned, P = principal, r = interest rate, t = time

 

The simple interest is 100,000(0.05)(2) = $10,000, so the amount earned after 2 years is $100,000 + 10,000 = $110,000

 

The formula for compound interest is A = P(1 + i)ⁿ, where A = the compound amount, P = principal, i = interest rate per period, n = the number of compounding periods

 

A = 100,000(1 + (0.05/12))²⁴ = $110,494.13

 

The difference in the two amounts is:

 

$110,494.13 - $110,000 = $494.13

 

The compound interest earns more