Question

Suppose you deposited $13000 in a saving account in which interest is compounded continuously. It takes 14 years to double your money in this account.(1) What is the annual rate of interest? (Round your answer to one decimal place.) % Tries 0/99(2) How much will you have in this account after 26 years? (Round your answer to two decimal places.) dollars Tries 0/99

Answer 1

Remember that

The formula to calculate continuously compounded interest is equal to

`A=P\left(e\right)^{\left\{rt\right\}}`

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 the Number of Time Periods

e is the mathematical constant number

In this problem, we have that

Part 1

P=$13,000

A=$26,000

t=14 years

substitute given values

`\begin{gathered} 26,000=13,000\left(e\right)^{\left\{14r\right\}} \\ solve\text{ for r} \\ 2=e^(14r) \\ apply\text{ ln on both sides} \\ ln(2)=lne^(14r) \\ ln(2)=14r \\ r=(ln(2))/(14) \\ \\ r=0.0495 \\ r=4.95\% \\ r=5\% \end{gathered}`

Part 2

we have

P=$13,000

r=5%=0.05

t=26 years

substitute in the formula