How long will it take for $800 to double if it is invested at 5% annual interest, compounded continuously?
A) It will take approximately 14.18 years.
B) It will take approximately 13.86 years.
C) It will take approximately 14.62 years.
D) It will take approximately 15.00 years.
E) It will take approximately 6.02 years.

Question

Quizplus · Accepted Answer

The formula to find the number of years it takes for an investment to double with continuous compounding is:
t = ln(2) / (r * 100)
where t is the number of years, ln is the natural logarithm, and r is the annual interest rate.

Plugging in the values, we get:
t = ln(2) / (5 * 100) = 0.01386 years

Multiplying by 12 to convert to months, we get:
t = 0.01386 * 12 = 0.16632 months

Multiplying by 30 to convert to days, we get:
t = 0.16632 * 30 = 4.9896 days

Rounding up to the nearest whole number, we get:
t = 5 days

Therefore, it will take approximately 13.86 years for $800 to double at 5% annual interest with continuous compounding.

How Long Will It Take for $800 to Double If