Question

1. Shroug w rok wants to invest AED 800.000 in cash to buy a new car 4 years from today. She expects to cam 7 percent per year, compounded annually on her savings. How much should she get to meet this purpose? 2. What is the present value of AED 45.000 deposited for 6 years at 10 percent per annum interest compounded annually? 3. If you wish to accumulate AED 200,000 in 5 years, how much must you deposit today in an account that pays an interest rate of 12% per annum compounded semiannually 4. How much will there be in an account at the end of 6 years if an amount of AED 12.000 is deposited today and the interest is 6% per year compounded quarterly, 5. Rashid has only AED 70,000 today but needs AED 100,000 to buy a new dream car. How long will he has to wait to buy the car if he can earn 10 percent per annum compounded annually on his savings?

Answer 1

1)	Future Value = Present Value*((1+r)^t)
	where r is the interest rate that is 7% and t is the time period in years that is 4.
	Future value = 800000
	800000 = Present value*((1.07)^4)
	800000 = Present value*((1.07)^4)
	Present value = 800000/(1.310796)
	Present value = 610316.2.
	Shrouq should get AED 610316 today to meet the purpose.

2)	Present value of an annuity = C[(1-(1/(1+r)^t))/r]
	where C is the annuity payment that is AED 45000.
	r is the interest rate that is 10%.
	t is the time period in years that is 6.
	Present value = 45000*[(1-(1/(1.10)^6))/.10]
	Present value = 45000*[(1-(1/(1.771561))/.10]
	Present value = 45000*[(1-.564474)/.10]
	Present value = 45000*[(.435526/.10]
	Present value = 45000*[(4.35526]
	Present value = 195986.7.
	The present value is AED 195986.7.

3)	Present Value = Future value/[(1+(r/m))^mt]
	Future value = 200000.
	r is the interest rate that is 12%.
	t is the time period in years that is 5.
	m is the compounding period that is 2.
	Present value = 200000/[(1+(.12/2))^5*2]
	Present value = 200000/[(1.06)^10]
	Present value = 200000/(1.790848)
	Present value = 111679.
	You must deposit AED 111679 in the account.

4)	Future Value = C*[(1+(r/m))^mt]
	where C is the present value that is 12000.
	r is the interest rate that is 6%.
	t is the time period in years that is 6.
	m is the compounding period that is 4.
	Future value = 12000*[(1+(.06/4))^4*6]
	Future value = 12000*[(1.015)^24]
	Future value = 12000*[1.429503]
	Future value = 17154.03.
	At the end of 6 years, there will be AED 17154 in the account.

5)	Future Value = Present Value*((1+r)^t)
	where r is the interest rate that is 10% and t is the time period in years.
	Present value	70000
	Future value	100000
	100000 = 70000*((1.10)^t)
	(1.10)^t = 100000/70000
	(1.10)^t = 1.428571
	Take natural log on both sides.
	tln(1.10) = ln(1.428571)
	t*(.09531) = .35667
	t = .35667/(.09531)
	t = 3.74.
	Rashid will have to wait for 3.74 years.

Answer 2

Huda deposited AED 30,000 into Abu Dhabi National Bank that pays interest of 8 % compounded Quarterly. How much will Huda have in her account at the end of 5 years?