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Recall that an annuity is any sequence of equal periodic payments. If payments are made at...

Recall that an annuity is any sequence of equal periodic payments. If payments are made at the end of each time interval, then the annuity is called an ordinary annuity. We consider only ordinary annuities in this summer. The amount, or future value, of an annuity is the sum of all payments plus all interest earned. Suppose you decide to deposit $600 every 6 months into an account that pays 18% compounded semiannually. If you make eight deposits, one at the end of each interest payment period, over 4 years, you like to know how much money will be in the account after the last deposit is made. Instead of simply plugging into the formula (attached at the last page), you are asked by the following questions:

(a) Think in terms of time line and use the compound amount formula A = P(1 + i) n , what will be the future value of the FIRST $600 payment?

(b) Again, use the compound amount formula A = P(1 + i) n , what will be the future value of the SECOND $600 payment?

(c) What will be the future value of the THIRD $600 payment?

(d) What will be the future value of the FOURTH $600 payment?

(e) What will be the future value of the FIFTH $600 payment?

(f) What will be the future value of the SIXTH $600 payment?

(g) What will be the future value of the SEVENTH $600 payment?

(h) What will be the future value of the EIGHTH (LAST) $600 payment?

(i) Now, adding all the eight future values above, how much money will be in the account after the last deposit is made? Compare this answer with the answer you use the formula.

Expert Solution

Requirement	Payment No.	Amount (p)	Semi-annual Rate (i)	Number of Periods Compounded (n)	*Maturity Value = p(1+i)^n**
a	1	600	0.0900	7.00	1096.82
b	2	600	0.0900	6.00	1006.26
c	3	600	0.0900	5.00	923.17
d	4	600	0.0900	4.00	846.95
e	5	600	0.0900	3.00	777.02
f	6	600	0.0900	2.00	712.86
g	7	600	0.0900	1.00	654.00
h	8	600	0.0900	0.00	600.00
i				Total of all Maturity Values	6617.08

Formula for Future Value Annuity Factor

Where FVA = Future Value Annuity

p=Periodic Payment

r = rate of Interest per period

n = number of periods payments to be made

Particulars	Calculation	Formula Notes
Semi Annual Payments (P)	600	<B11
Number of Years	4	<B12
Annual Interest Rate	18.00%	<B13
Number of Payments per years( Given Monthly)	2	<B14
Number of Monthly Payments (Years*12) (n)	8	=B12*B14
Monthly Interest Rate (Annual Interest Rate /12) (r)	9.000%	=B13/B14
FVA = Money after 10 Years	6617.08	=B11*(((1+B16)^B15-1)/B16)

Maturity Value calculated from formula and table are equal.

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jeff jeffy answered 2 years ago

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