Question

If $600 is deposited into a savings account which pays 4.8% interest, compound continuously (A = Pe^rt), how long will it take the money to triple. Round to the nearest tenth of a year.

Answer 1

`22.9\ years`

Explanation:

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

`t=?\ years\\ P=\$600\\ r=0.048\\ A=\$600*3=\$1,800`

substitute in the formula above and solve for t

`\$1,800=\$600(e)^(0.048t)`

Simplify

`3=(e)^(0.048t)`

apply ln both sides

Remember that

`ln(e)=1`

`ln(3)=0.048t*ln(e)`

`ln(3)=0.048t`

`t=ln(3)/0.048=22.9\ years`