ASSUME COMPOUND INTEREST EXCEPT WHERE NOTED APPROXIMATELY HOW MANY YEARS WILL IT
ID: 1169752 • Letter: A
Question
ASSUME COMPOUND INTEREST EXCEPT WHERE NOTED
APPROXIMATELY HOW MANY YEARS WILL IT TAKE TO DOUBLE AN INVESTMENT AT A 4% ANNUAL COMPOUND INTEREST RATE?
A STUDENT DECIDES TO TAKE A YEAR OFF SCHOOL TO SAVE ENOUGH MONEY FOR THE NEXT ACADEMIC YEAR. THE STUDENT IS LIVING WITH HIS IN-LAWS AND PLANS TO SAVE ALL OF THE EARNED MONEY. THE INTEREST RATE IS 1.5% PER MONTH COMPOUNDED WEEKLY. THE STUDENT NEEDS $8500 TO FINANCE THE NEXT ACADEMIC YEAR. HOW MUCH MONEY WILL THE STUDENT HAVE TO EARN DURING THE NEXT 12 MONTHS FOR STUDY THE FOLLOWING YEAR AT ISU?
A GOLD MINE IS PROJECTED TO PRODUCE $200,000 DURING ITS FIRST YEAR OF OPERATION, $190,000 THE SECOND YEAR, $180,000 THE THIRD YEAR AND SO ON TO YEAR 10. IF THE ANNUAL INTEREST RATE IS 5%, WHAT IS THE PRESENT WORTH OF THE MINE?
4A. WHAT IS THE ANNUAL WORTH OF THE GOLD PRODUCTION IN PROBLEM 3?
4B. WHAT IS THE FUTURE WORTH OF THE GOLD PRODUCTION IN PROBLEM 3?
A WAREHOUSE WAS PURCHASED 10 YEARS AGO FOR $250,000. SINCE THEN, THE ANNUAL INTEREST RATE HAS BEEN 5% AND INFLATION HAS HELD STEADY AT 2%/YEAR. WHAT SHOULD THE WAREHOUSE SELL FOR AT TODAY’S VALUE?
FIFTEEN YEARS AGO $1000 WAS DEPOSITED IN A BANK ACCOUNT. TODAY THE DEPOSIT IS WORTH $2300. WHAT WAS THE ANNUAL INTEREST RATE PAID ON THE ACCOUNT?
SIGN THE LAST PAGE MAKING THE STATEMENT THAT YOU HAVE WORKED ALONE AND N OT WITH ANY OTHER STUDENT ON THIS ASSIGNMENT.
Explanation / Answer
1) We can use Rule of 72 here. Divide 72 by interest rate and it will give you number of years required to double the investment.
So 72/4=13. It will take 13 years to double the amount at 4%.
2) The amount required is 8500 and interest is given as 18% per annum compunded weekly.
So 8500/ (1+0.18/52)^52 = 7102
3) We will have to discount the cash flow to get the present value
200000/(1.05) + 190000/(1.05)^2 + 180000/(1.05)^3..........
3a) Annual worth in each year is given below
3b) There seems to be some insufficient data. Initial outgo of funds is not mentioned.
4) The real interest rate is approximately 3% (5%-2%).
2500*(1.03)^10 = 3359.79
5) (2300/1000)^1/15
= 1.0571
Now (1.0571-1)*100
=5.71%
=1418030