Question

Andy deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Barb also deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Andy will withdraw his interest earnings and spend it as soon as possible. Barb will reinvest her interest earnings into her account. Given this, which one of the following statements is true?a. ​Barb will earn more interest the second year than Andy.b. Andy will earn more interest in year three than Barb will.c. ​Barb will earn more interest the first year than Andy will.d. ​Andy will earn compound interest.e. ​After five years, Andy and Barb will both have earned the same amount of interest.

Answer 1

Answer:

A. Barb will earn $7.5 more interest in the next year than Andy

Explanation:

Compound interest applies on the reinvested interest amount.

Solution:

Andy's earning:

F= Future Value , P = Present Value, i = Interest rate, n=Years

Using = F = P(1+i)∧ n

First Year:

F = $3,000(1 + 0.05)∧1

   = $3,150

Interest Earning:

$3,150 - $3,000 = $150

Second Year

F = $3,000(1 + 0.05)∧1

   = $3,150

Interest Earning:

$3,150 - $3,000 = $150

Interest Earning Total = $150 + $150 = $300

Barb's Earnings:

For First year,

F = $3,000(1+0.05)∧ 1

  = $3,150

Interest Earning:

$3,150 - $3000 = $150

For Second year,

F = $3,150(1.05)∧ 1

  = $3,307.5

Interest Earning:

$3,307.5 - $3150 = $157.5

Interest Earning Total = $150 + $157.5 = $307.5

Barb's Earnings - Andy's Earnings = $307.5 - $300  = $7.5