Question

A. A $10,000 certificate of deposit earns simple interest of 8 percent per year. Calculate the total earned money over the 5 year period?
B. A sum of $22,000 is invested in a savings account which pays interest at the rate of 7 percent per year compounded quarterly. If the amount is kept on deposit for 10 years, what will the compound amount equal? How much interest will be earned during the 10 Years. Also calculate the effective interest rate.
C. A Company wants to deposit $1,000,000 per year in an investment which earns interest of 10 percent per year. Assume the first deposit is made at the end of the current year and addidtional deposits at the end of each following year.
a) To what sum will the investment grow at the time of the 10th deposit?
b) How much interest will be earned.
D. A person wants to generate eight intallments of $1,000 in the following four years. How much money should be invested, if the interest rate is 10 percent per year.

Answer 1

A)Calculation of the total earned money over the 5 year period

Deposit Amount = $ 10,000

Rate of interest = 8% per year.

Term = 5 years

Interest earned = PTR/100

Where p = Principal , T = Time , R = Rate of interest

Interest earned over the 5 year period = ($ 10,000*5*8)/100

=$ 4000

Total amount = Principal + Interest = $ 10,000+ $ 4000 = $ 14000

B) Deposit Amount = $ 22000

Rate of interest = 7% Compounded Quarterly

Deposit term = 10 years

We know that Future value = Present value ( 1+i/4)^4n

Where n = No.of years , i= Rate of interest

Future value = $ 22000( 1+7/400)^4*10

= $ 22000( 1.0175)^40

= $ 22000*2.001597

= $ 44035.13

Hence the Compounded Amount is $ 44035.13

Effective interest rate = [( 1+i/m ) ^m - 1]*100

Here m = Compounding Frequency per year i.e 4 times

= [ ( 1+7/400)^4 - 1 ] *100

= [1.0175^4 - 1 ]*100

= 0.071859

= 7.1859%

Effective Annual interest rate is 7.1859%

C)

Year	Opening Balance	Interest @ 10%	Total amount	Amount Deposited	Closing Balance
1				$1,000,000	$1,000,000
2	$1,000,000	$100,000.0	$1,100,000.0	$1,000,000	$2,100,000.0
3	$2,100,000.0	$210,000.0	$2,310,000.0	$1,000,000	$3,310,000.0
4	$3,310,000.0	$331,000.0	$3,641,000.0	$1,000,000	$4,641,000.0
5	$4,641,000.0	$464,100.0	$5,105,100.0	$1,000,000	$6,105,100.0
6	$6,105,100.0	$610,510.0	$6,715,610.0	$1,000,000	$7,715,610.0
7	$7,715,610.0	$771,561.0	$8,487,171.0	$1,000,000	$9,487,171.0
8	$9,487,171.0	$948,717.1	$10,435,888.1	$1,000,000	$11,435,888.1
9	$11,435,888.1	$1,143,588.8	$12,579,476.9	$1,000,000	$13,579,476.9
10	$13,579,476.9	$1,357,947.7	$14,937,424.6	$1,000,000	$15,937,424.6
	Total	$5,937,424.6

a So the investment amount will become to $ 159,37424.6

b Interest earned = $ 59,37424.6

D ) Calculation of Present value of a Annuity

Annuity * PVAF = Present value

$ 1000* PVAF ( 10% , 4 ) = Present value

Present value = $ 1000*3.169865

Present value = $ 3169.865.

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