Question

Wynona, decides that she will invest $5,000 per year in a 5% annuity for the first ten years, then $6,000 for the next ten years, and then $4,000 per year for the last ten years, how much will she accumulate? [Hint: Treat each ten-year period as as separate annuity and compute the Future Value. After the ten years, assume that the value will continue to grow at compound interest for the remaining years of the 30 years.Answer: 10x1=10 5%/1=5% table value=1.62889

5000(1.62889) = 8144.45
6000(1.62889) = 9773.34
4000(1.62889) = 6515.56
= 24433.35

Answer 1

For 1st 10 years the sum looks like this:
\[5000(1+1.05+...1.05^{9}) = 5000\frac{1.05^{10}-1}{1.05-1} = 62,889.46\]
this will then earn interest for next 20 years
\[\rightarrow 62,889.46(1.05)^{20} = 166,864.47\]
For next 10 years investing 6000 per year
\[6000\frac{1.05^{10}-1}{1.05-1} = 75,467.36\]
this will earn interest for final 10 years
\[\rightarrow 75,467.36(1.05)^{10} = 122,928.37\]
Last 10 years invest 4000 per year
\[4000\frac{1.05^{10}-1}{1.05-1} = 50,311.57\]
For a total sum of:
\[166,864.47+122,928.37+50,311.57 = 340,104.41\]

Answer 2

boy,
i wasnt even close

Answer 3

thanks for taking the time to help,

Answer 4

no problem