Question

As the Head of Research & Development for a young start-up organiza always trying to manage large capital investments to maintain a sufficient a it for a young start-up organization, you are pital investments to maintain a sufficient amount of liquid (i.e. easily spendable) cash. Your team has recommended the purchase of a new machine that will cost $98,000 to purchase. This price has been guaranteed by the vendor for the next 8 years (I.e. the machine will cost $98,000 to purchase regardless of which year between now and the start of year 8 in which the machine is purchased). After this time, the price will increase to $128,000 which will be honored for any year of purchase starting in year 9. All purchases will be made at the end of the year and all deposits will be made at the start of the year. a. [2 points if your company was to place $3800 into a savings account at the end of year 1 and every year thereafter until the purchase is made, and that account earns 7.33% interest per year, in what year (remember purchases are made at the end of the year only!) will you be able to purchase the machine? How much will the machine cost at the time of purchase? h 12 points. Assume that your company will need to purchase the machine by the end of the vear 7. How much would you need to deposit today, and at the end of each year Iyears 1 through 7) in order to have enough ugh 71 in order to have enough money saved for the purchase? Once again, assume osits are equal in size and that they are made into the same account that earns 7.33% interest per year.

Answer 1

a. He will be able to purchase the machine in 28 years time, when he should have saved up to $130,140 for the sume of $128,000. Because he will not have saved up to $98,000 in 8 years time.

b. The machine will cost $128,000 at the time of purchase, because they was no agreed increment of price after 9 years. Even though he has saved up to $130,140.7

c. If he wish to buy the machine in 7years, when the machine is sold at $98,000 he will need to save $13,000 yearly. By 7 years he would have saved $99,330

Explanation:

A. Which year will he buy the machine.

We will be solving this yearly.

For the first year:

Interest is $3,800×7.33%= $278.54

Total cash is $3,800+$278.54= $4,078.53

For the second year:

Interest accumulated is ($4,078.54+$3,800)7.33%= $577.497

Total cash is $4,078.53+$3,800+$577.497= $8,456.04

Because this method is going to take more time, his savings is not likely to be up to $98,000 in 8 years time.

Therefore we will use the try and error method, using the compound interest formula.

Compound interest=P[(1+i)^n -1]

P= principal, i=interest rate per year, n=number of years

Let's assume he bought the machine in 27th year.

Compound interest is; $3,800[(1+0.0733)^27 -1) = $21,859.5

Total deposit is; $3,800×27= $102,600

Total cash saved is; $21,859.5+$102,600= $124,459

This is not enough to buy the machine.

Let's assume he bought the machine in the 28th year.

3800[(1+0.0733)^28 -1]= $23,740

Total deposit is; $3,800× 28= $106,400

Total cash saved; $106,400+$23,740= $130,140

Since he will save up to $130,140 in the 28 year, he will be able to purchase the machine for $128,000

C. How much he will deposit yearly to be able to buy the machine in 7year time, which will cost $98,000.

Let assume interest is not applied he will save; $98,000/7 =$14,000 yearly.

With this assumptions we can assume faster.

Let assume interest is applied. And he saves $13,000 yearly.

compounded interest is; $13,000[(1+0.0733)^7 -1]= $8,330.02

Total deposit is; $13,000×7=$91,000

Total cash saved; $8,330.02+$91,000=$99,330

This means he will be able to save up to $98,000 by the end of the 7th year, to acquire the machine.