1 Convert the following cash flow below to a future value at

1. Convert the following cash flow below to a future value at year 7. Let i per year? EOY 3 0 2 6 7 $100 S100 $100 $100 $100 $100 $200 Engineers at Sea World, a division of Busch Gardens, Inc., have completed an innovation on an existing water sports ride to make it more exciting. The modification costs only $8000 and is expected to last 6 years with a $1300 salvage value for the solenoid mechanisms. The maintenance cost is expected to be high at $1700 the first year, increasing by 11% per year thereafter. Determine the equivalent present worth of the modification and maintenance cost. The interest rate is 8% per year 2. 3. Use the cash flow diagram to determine the single amount of money Qs in year 4 that is equivalent of to all cash flow shown. Use i-10% per year. 1 0 7 8 year S25 $25 $25 $25 $25 $25 $25 S50 $50 $50 What will be the required annual payment to repay a loan of $3000 in 3 years if the interest rate is 9% compounded continuously? 4. What is the present value of the following equal annual receipts: $700 per year for 10 years at 12% compounded continuously. 5. 6. What is the accumulated value of the following series of payments: $400 at the end of each year for 5 years at 9.8% interest compounded continuously.

Solution

1).

Consider the given problem here the cash flow are given in the problem. So, given the cash flow and the rate of interest rate the future value is given below.

=> FV = 100*(1.09)^7 + 100*(1.09)^6 + 100*(1.09)^5 + 200*(1.09)^4 + 100*(1.09)^3 + 100*(1.09)^2 + 100*(1.09)^1.

=> FV = 182.8039 + 167.71 + 153.8624 + 282.3163 + 129.5029 + 118.81 + 109 = 1,144.0055.

=> FV = 1,144.

2).

Now, here the “modification cost” is “8000” and the maintenance cost is “1,700”in the 1^st year and increases by “11%” per year thereafter.

=> the present value of the “modification cost” and “maintenance cost” is given by.

=> 8000 + 1700/1.08 + 1700/1.08^2 + 1700/1.08^3 + 1700/1.08^4 + 1700/1.08^5 + 1700/1.08^6.

=> PV = 8,000 + 1,574.0741 + 1,457.4760 + 1,349.5148 + 1,249.5507 + 1,156.9914 + 1,071.2884 = 15,858.89 = 15,859.