Question

Question 2 2 pts Suppose Mr. Smith contracted with Roles Rice, Inc., to take delivery on a car in four years for $142,500. An initial deposit of $34,000 has been paid at the time of the contract, and the rest will be paid at the time of delivery (four years from now). Mr. Smith went to his bank and deposited a sum, $A. He made a promise to himself that he would withdraw half the accumulated amount from this account each year. At the time of delivery, there must be exactly $108,500 in the account to pay for the car. How much money must Mr. Smith deposit in his account to have the required amount at the time of delivery? (Assume a 13 percent annual interest rate.) Round your final answer to two decimal places. See Example 4.3 if you haven't already. Question 3 2 pts In how many years will $100 grow to $1,000 at annual rates of interest of 24%? Round your final answer to the larger integer. (9.3 years means 10 years)

Answer 1

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