You deposit $1,000.00 into a savings account for 4 years
at an interest rate of 7 per cent compounded continuously.

How much money do you have after 4 years?

Total = 1,000 * 2.718281828459 ^{(.07 • 4)}
Total = 1,000 * 1.32312981233744
Total = 1,323.13

After 11 years at a 6.25% continuously compounded rate,
you now have $13,752.38.

How much money did you start with?

Principal = 13,752.38 ÷ 2.718281828459 ^{(.0625 • 11)}
Principal = 13,752.38 ÷ 1.9887374696
Principal = 6,915.13

You have invested $2,750.00 at a
continuously compounded rate of 8.15%.

How long will it take for this to become $10,000?

Years = ln(10,000 / 2,750) ÷ .0815
Years = ln(3.6363636363636) ÷ .0815
Years = 1.29098418131557 ÷ .0815
Years = 15.8402967032585
About 15.84 years (rounded)

You have invested $4,000.00 and would like it to become $10,000.00 in 10 years.

What continouously compounded interest rate is required?

rate = ln(10,000 / 4,000) ÷ 10
rate = ln(2.5) ÷ 10
rate = 0.9162907319 ÷ 10
rate = 0.09162907319 or 9.162907319%