Question

Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They substitute their values shown below into the compound interest formula. Compound interest accounts name principal interest rate number of years compounded Jaina $300 7% 3 once a year Tomas $400 4% 3 once a year a = p (1 + r)³ Which pair of equations would correctly calculate their compound interests?

1) Jaina: a = 400 (1 + 0.07)³, Tomas: a = 300 (1 + 0.04)³
2) Jaina: a = 300 (1 + 0.03)⁷, Tomas: a = 400 (1 + 0.03)⁴
3) Jaina: a = 400 (1 + 0.03)⁷, Tomas: a = 300 (1 + 0.03)⁴
4) Jaina: a = 300 (1 + 0.07)³, Tomas: a = 400 (1 + 0.04)³

Answer 1

The correct equations for calculating Jaina and Tomas's compound interests are Jaina: a = 300 (1 + 0.07)^3, and Tomas: a = 400 (1 + 0.04)^3, which corresponds to option 4 from the choices given.

Step-by-step explanation:

When Jaina and Tomas compare their compound interest accounts to see how much they will have in their accounts after three years, they will use the formula a = p (1 + r)^t where a is the amount of money accumulated after n years, including interest, p is the principal amount, r is the annual interest rate (decimal), and t is the time the money is invested for, in years.

For Jaina, the correct substitution should include her principal of $300, interest rate of 7% (as a decimal 0.07), and number of years which is 3. The correct equation for Jaina is therefore a = 300 (1 + 0.07)^3.

For Tomas, the correct substitution should include his principal of $400, interest rate of 4% (as a decimal 0.04), and number of years which is 3. The correct equation for Tomas is therefore a = 400 (1 + 0.04)^3.

Thus, the pair of equations that would correctly calculate their compound interests is option 4): Jaina: a = 300 (1 + 0.07)^3, Tomas: a = 400 (1 + 0.04)^3.