Question

Payments of $1000 are invested into an account at the end of each year for 8 years, earning 8% effective per annum. Interests can only be reinvested at 6% for the first 6 years and 7% thereafter. Find the accumulated value of the investment after 10 years. (Answer: $12092.96)

Answer 1

The accumulated value = $12092.97

The following table expalins the working of the cash flow

Year	Investment 'A'	Interest Earned B = Prev year Closing Bal X 8%	Closing Balance 'C' = A + Previous Year C	Interest on Interest reinvested D = Previous Year E x 6% (1st 6)0r 7% (later)	Closing Balance of Reinvested Interest and Income E = B + D + Prev Year E	Explanation
1	1,000.00	-	1,000.00			No interest earned as Investment done at year end
2	1,000.00	80.00	2,000.00	-	80.00	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end to earn 6%
3	1,000.00	160.00	3,000.00	4.80	244.80	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 6%
4	1,000.00	240.00	4,000.00	14.69	499.49	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 6%
5	1,000.00	320.00	5,000.00	29.97	849.46	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 6%
6	1,000.00	400.00	6,000.00	50.97	1,300.42	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 6%
7	1,000.00	480.00	7,000.00	91.03	1,871.45	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 7%
8	1,000.00	560.00	8,000.00	131.00	10,562.46	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 7%
9				739.37	11,301.83	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 7%
10				791.13	12,092.96	Interest (8%) is earned on Closing Balance C at year end & is reinvested at year end (E) to earn 7%