Find the missing values assuming continuously compounded interest.

Question

Initial Investment = 1000

Annual = 5.6%

Time to double = ?

Amount after 10 years = ?

Answer 1

the underlying formula that you want to use here for continuous compounding is

A = P*e^(rt)

for this scenario that means taking

A = 1000 * e^(0.056*10)

A = 1750.67

meaning that the accumulated amount in the account after 10 years is $1,750.67

then for doubling time you can take

t = ln(2) / r

t = ln(2) / 0.056 = 12.38 years

Answer 2

2 =e^.056t

ln2 = .056t

t = ln2/.056

t = about 12.378 years doubling time

in 10 years

A=1000e^.056(10)

= 1000e^.56

= $1,750.67

in about 12 years 1000 becomes 2000

so in 10 years, 1000 becomes a little less than 2000,

as 10 is a little less than 12. 1750.67 is in the right range

use a calculator with a natural log function and inverse