twelve deposits of $1,000 are made at the end of every quarter at an interest rate...

twelve deposits of $1,000 are made at the end of every quarter at an interest rate of 10% compounded quarterly. (case A) and another deposit of $2,000 is made every six months at an interest rate of 12% for three years. case B

A.) show the cash flow diagram for both cases
b.) what is the accumulation after 3 years for each case?
C.) what is the effective interest rate for each case?
D.) which case is better?

Expert Solution

Cash flow:

Year	0.25	0.5	0.75	1	1.25	1.5	1.75	2	2.25	2.5	2.75	3
Case A	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00	$ 1,000.00
Case B		$ 2,000.00		$ 2,000.00		$ 2,000.00		$ 2,000.00		$ 2,000.00		$ 2,000.00

	Case A	Case b
0.25	$ 1,000.00
0.5	$ 1,000.00	$ 2,000.00
0.75	$ 1,000.00
1	$ 1,000.00	$ 2,000.00
1.25	$ 1,000.00
1.5	$ 1,000.00	$ 2,000.00
1.75	$ 1,000.00
2	$ 1,000.00	$ 2,000.00
2.25	$ 1,000.00
2.5	$ 1,000.00	$ 2,000.00
2.75	$ 1,000.00
3	$ 1,000.00	$ 2,000.00

FV	$ 13,795.55	$ 13,950.64
PV	$ 10,257.76	$ 9,834.65
1+Rate	1.10381289	1.1236
Effective rate	10.38%	12.36%

Accumulation after 3 years = Future value after 3 years:
Excel formula:
CAse A: =FV(0.025,12,-1000)
Case B: =FV(0.06,6,-2000)

c) Effective interest rate annually= (FV/PV)^1/n where n is number of years or 3 in this case

CAse A: 10.38%
CAse B:12.36%

D) Since the effective rate of case b is better one should invest in case B

jeff jeffy answered 2 years ago

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