Faith invested $350 in an account paying an interest rate of 4 5/8% compounded monthly. Kevin invested $350 in an account paying an interest rate of 4 7/8% compounded continuously. To the nearest hundredth of a year, how much longer would it take for Faith's money to double than for Kevin's money to double?

It would take 0.8 years longer for Faith's money to double than for Kevin's money to double.

Step-by-step explanation:

We are to find the time it would take for each person's money to double and we would be making use of compound interest formula to solve for this

For Faith

Faith invested $350 in an account paying an interest rate of 4 5/8% compounded monthly.

Double $350 = $700

Interest rate = 4 5/8%

= 4.625%

First, convert R as a percent to r as a decimal

r = R/100

r = 4.625/100

r = 0.04625 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(700.00/350.00) / ( 12 × [ln(1 + 0.04625/12)] )

t = ln(700.00/350.00) / ( 12 × [ln(1 + 0.003854167)] )

t = 15.016 years

Therefore, it would take 15.016 years for Faith's money to double

For Kelvin

Double $350 = $700

Kevin invested $350 in an account paying an interest rate of 4 7/8% compounded continuously.

Interest rate = 4.875%

First, convert R as a percent to r as a decimal

r = R/100

r = 4.875/100

r = 0.04875 per year,

Then, solve the equation for t

t = ln(A/P) / r

t = ln(700.00/350.00) / 0.04875

t = 14.218 years

Therefore, it would take 14.218 years for Kelvin's money to double.

To the nearest hundredth of a year, how longer would it take for Faith's money to double than for Kevin's money to double is calculated as

15.016 years - 14.218 years

= 0.798 years

Approximately to the nearest hundredth ≈ 0.80 years

Therefore, it would 0.8 years longer for Faith's money to double than for Kevin's money to double.