Question

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?

Answer 1

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

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.