Answer:
2) let Smith deposited A amount in bank account
So After 1 year this amount =A*(1+13%)^1=1.13A
Since he withdraw half of amount so amount left in bank account=0.5*1.13A=0.565A
After 2 nd year amount in bank=1.13*0.565A=0.63845A
Since he withdraw half of amount so amount left in bank account=0.5*0.63845A=0.319225A
After 3rd year amount in bank=1.13*0.319225A=0.36072425A
Since he withdraw half of amount so amount left in bank account=0.5*0.0.36072425A=0.180362125A
After 4th year amount in bank=1.13*0.180362125A=0.234470763A
Since 0.234470763A=108500
A=$462744.26
So Smith deposited $462744.26 in his bank account.
3)
Given
A=$100
F=$1000
r=24%
So
F=A*((1+r)^n-1)/r
1000=100*((1+24%)^n-1)/24%
(1+24%)^n=3.4
n*(ln(1.24)=ln(3.4)
n=5.68 years =6 years
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