Question

Tyson and Ariana each invested $2,500 in separate accounts. Tyson’s interest rate is 5.75% and is compounded annually. Ariana’s simple interest rate is 5.75%. Neither will make any additional deposits or withdrawals. At the end of 6 years, how much more has Tyson earned? Round your answer to the nearest cent.

Answer 1

Tyson's account will have $ 133.90 more than Ariana's account.

Explanation:

In Tyson's case, he invests $ 2,500 in an account whose interest rate is 5.75% and is compounded annually. In turn, Ariana invests the same amount and for the same interest, but this is not compounded.

Thus, Ariana, at the end of her 6 years, will have a total amount in her account of $ 3,362.5 (((2,500 x 5.75 / 100) x 6) + 2,500), of which $ 862.5 will correspond to the interest generated.

Instead, Tyson's investment interests will be consolidated annually. Thus, in 6 years, this investment will evolve as follows:

-Year 1 --- 2,500 x 1.0575 = 2,643.75

-Year 2 --- 2,643.75 x 1.0575 = 2,795.76

-Year 3 --- 2,795.76 x 1.0575 = 2,956.52

-Year 4 --- 2,956.52 x 1.0575 = 3,126.52

-Year 5 --- 3,126.52 x 1.0575 = 3,306.29

-Year 6 --- 3,306.29 x 1.0575 = 3,496.40

Thus, at the end of the 6 years, Tyson will have $ 3,496.40 in his account. Thus, Tyson's account will have $ 133.90 more than Ariana's account.