Answer:
5.67 years
8.99 years
Step-by-step explanation:
The relationship between future value, present value, interest rate as well as the duration of an investment(n) are depicted below with future value formula:
FV=PV*(1+r)^n
FV=future value( let us assume it is $10,000)
PV=$5,000( half of the present value)
r=13% interest rate
n=duration of the investment=the unknown
10,000=5000*(1+13%)^n
10,000/5000=1.13^n
2=1.13^n
take log of both sides
ln(2)=n ln(1.13)
n= ln(2)/ln (1.13) = 5.67 years
Triple of original investment:
FV=PV*(1+r)^n
FV=future value( let us assume it is $15,000)
PV=$5,000(one-third of the present value)
r=13% interest rate
n=duration of the investment=the unknown
15,000=5000*(1+13%)^n
15,000/5000=1.13^n
3=1.13^n
take log of both sides
ln(3)=n ln(1.13)
n= ln(3)/ln (1.13) = 8.99 years