Question

Please help ASAP

Find how long it takes $1500 to double if it is invested at 7% interest compound semiannually. Use the formula A=P (1+r/n)^nt to solve the compound interest problem.

It will take approximately ? Years .
Round to the nearest tenth as needed.

Answer 1

`A=P(1+ (r)/(n))^ (t)/(n)`
A=future amount
P=present amount
r=rate in decimal
n=number of times per year compounded
t=time in years

how many years to double
basically
A=2P at t=?
so we can simplify and ignore the pricipal given and do

`2=(1+ (r)/(n))^ (t)/(n)`
r=7%=0.07
n=2 (semiannualy means 2 times per year)
t=t


`2=(1+ (0.07)/(2))^ (t)/(2)`

`2=(1+ 0.035)^ (t)/(2)`

`2=(1.035)^ (t)/(2)`
take the ln of both sides

`ln2=((t)/(2))ln1.035`
divide both sides by ln1.035

`(ln2)/(ln1.035) = (t)/(2)`
times 2 both sides

`(2ln2)/(ln1.035) =t`
use calculator
40.2976=t
nearest tenth
40.3
about 40.3 years