Answer:
[tex]n\approx \ 13 \ months[/tex]
Step-by-step explanation:
#We find the effective annual interest rate given 10% compounded monthly:
[tex]i_m=(1+i/m)^m-1, m=12, i=0.10\\\\i_m=(1+0.1/12)^{12}-1\\\\=0.104713[/tex]
#find the sum of future values of $14000 after 8 months and $15000 after 14 months using [tex]i_m[/tex]:
[tex]\sum FV={P(1+i_m)^n}_1+{P(1+i_m)^n}_2\\\\=14000(1.104713)^{8/12}+15000(1.104713)^{14/12}\\\\=14961.01+16848.02\\\\=31809.03[/tex]
#The future value of the single payment should be equal to the future value of the partial payments at [tex]i_m[/tex]:
[tex]31809.03=29000(1.104713)^n\\\\1.0968631=1.104713^n\\\\n=(log\ 1.104713)/(log \ 1.0968631)\\\\n=1.077131996\times 12 \ months \\\\n\approx 13 \ months[/tex]
Hence, the single payment has to be made approximately 13 months from now.
