Suppose a deposit of $500 is made at the beginning of each year for 25 years into an account that pays 11% compounded annually. What is the amount of this annuity at the end of the 25th year?
Answers:
I suggest making a table.
.... Beginning of ... End of .
.... Year Amount .... Year Amount
------------------------------...
Year 1 .. $500 ... x 1.11 = $555
** now for Year 2... you take the result at END OF Year 1 and ADD $500 . then take that NEW result and multiply by 1.11 to get the amount of annuity at the END OF Year 2 ... like this. (look at calculation for Year 2) **
Year 2 ($555+$500) x 1.11 = $1,171.05
** and for each successive year... you take the result at END OF the PREVIOUS year and ADD $500 . then take that NEW result and multiply by 1.11 to get the amount of annuity at the END OF the new "current" year ... like this. (look at calculation for Year 3 **
Year 3 ($1,171.05 + $500) x 1.11 = $1,854.87
** now look at the calculation for Year 4... Previous Year (Year 3) END OF year amount PLUS $500 . then multiply that new result by 1.11 ... and so on so for... for Year 5... for Year 6. all the way to Year 25. But remember... you have to ADD $500 first to the end of year amount of the previous year. because the problem states that you are depositing $500 at the beginning of EVERY YEAR. You have to add $500 first. THEN multiply the new amount by the 1.11...**
Year 4 ($1,854.87 + $500) x 1.11 = $2,613.90
Year 5 ($2,613.90 + $500) x 1.11 = $3,456.43
Year 6 ($3,456.43 + $500) x 1.11 = $4,391.64
Year 7 ($4,391.64 + $500) x 1.11 = $5,429.72
Year 8 ($5,429.72 + $500) x 1.11 = $6,581.99
Year 9 ($6,581.99 + $500) x 1.11 = $7,861.00
Year 10 ($7,861.00 + $500) x 1.11 = $9,280.72
Year 11 ($9,280.72 + $500) x 1.11 = $10,856.59
Year 12 ($10,856.59 + $500) x 1.11 = $12,605.82
Year 13 ($12,605.82 + $500) x 1.11 = $14,547.46
Year 14 ($14,547.46 + $500) x 1.11 = $16,702.68
Year 15 ($16,702.68 + $500) x 1.11 = $19,094.97
Year 16 ($19,094.97 + $500) x 1.11 = $21,750.42
Year 17 ($21,750.42 + $500) x 1.11 = $24,697.97
Year 18 ($24,697.97 + $500) x 1.11 = $27,969.74
Year 19 ($27,969.74 + $500) x 1.11 = $31,601.42
Year 20 ($31,601.42 + $500) x 1.11 = $35,632.57
Year 21 ($35,632.57 + $500) x 1.11 = $40,107.16
Year 22 ($40,107.16 + $500) x 1.11 = $45,073.94
Year 23 ($45,073.94 + $500) x 1.11 = $50,587.08
Year 24 ($50,587.08 + $500) x 1.11 = $56,706.65
Year 25 ($56,706.65 + $500) x 1.11 = $63,499.39
Hence, the amount of this annuity at the end of the 25th year is $63,499.39
Hope this helps!
take 500, multiple by 1.11, round off anything less than a penny and repeat 24 more times.
Here is the basic idea of what you need to do
first year 500 x .11 = 55 then add the original 500 to get 555
2nd 555 x .11 =61.05 adding principal to get 616.05
3rd 616.05 x .11= 67.77 ...... 683.82
4th 683.82 x .11=........
continue this all the way up to year 25.
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