Allison invests $100 at a 2% interest rate compounded continuously for 20 years. Maria invests $125 at a 1% interest rate compounded continuously for 15 years. Whose account has the highest balance at the end of its given investment period?

Allison has the highest balance at the end of its given investment period.

Step-by-step explanation:

For Allison,

FV = PV e⁽ⁿˣ⁾

FV = Future Value = ?

PV = Present Value = $100

n = Interest Rate = 2%

x = time in years = 20

e = mathematical constant = 2.7183

So,

FV = 100 x 2.7183⁽⁰°⁰² ˣ ²⁰⁾

FV = 100 x 2.7183⁽⁰°⁴⁾

FV = 100 x 1.4918

FV = $149.18

For Maria,

FV = PV e⁽ⁿˣ⁾

FV = Future Value = ?

PV = Present Value = $125

n = Interest Rate = 1%

x = time in years = 15

e = mathematical constant = 2.7183

So,

FV = 125 x 2.7183⁽⁰°⁰¹ ˣ ¹⁵⁾

FV = 125 x 2.7183⁽⁰°¹⁵⁾

FV = 125 x 1.1618

FV = $145.23

Since at the end of given investment period Allison has $149.18 and Maria has $145.23. So Allison has the highest balance.