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An amount if $ 2000 is invested at an interest of 5% per month. if $ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount have accumulated first exceed $ 42000.

Correct result:

n =  42

Solution:

x0=2000 x1=x0 1.05+200=2000 1.05+200=2300 x2=x1 1.05+200=2300 1.05+200=2615 x3=x2 1.05+200=2615 1.05+200=117834=2945.75 x4=x3 1.05+200=2945.75 1.05+200=3293.0375 x5=x4 1.05+200=3293.0375 1.05+2003657.6894 x6=x5 1.05+200=3657.6894 1.05+2004040.5738 x7=x6 1.05+200=4040.5738 1.05+2004442.6025 x8=x7 1.05+200=4442.6025 1.05+2004864.7327 x9=x8 1.05+200=4864.7327 1.05+2005307.9693 x10=x9 1.05+200=5307.9693 1.05+2005773.3678 x11=x10 1.05+200=5773.3678 1.05+2006262.0361 x12=x11 1.05+200=6262.0361 1.05+2006775.138 x13=x12 1.05+200=6775.138 1.05+2007313.8949 x14=x13 1.05+200=7313.8949 1.05+2007879.5896 x15=x14 1.05+200=7879.5896 1.05+2008473.5691 x16=x15 1.05+200=8473.5691 1.05+2009097.2475 x17=x16 1.05+200=9097.2475 1.05+2009752.1099 x18=x17 1.05+200=9752.1099 1.05+20010439.7154 x19=x18 1.05+200=10439.7154 1.05+20011161.7012 x20=x19 1.05+200=11161.7012 1.05+20011919.7862 x21=x20 1.05+200=11919.7862 1.05+20012715.7755 x22=x21 1.05+200=12715.7755 1.05+20013551.5643 x23=x22 1.05+200=13551.5643 1.05+20014429.1425 x24=x23 1.05+200=14429.1425 1.05+20015350.5997 x25=x24 1.05+200=15350.5997 1.05+20016318.1296 x26=x25 1.05+200=16318.1296 1.05+20017334.0361 x27=x26 1.05+200=17334.0361 1.05+20018400.7379 x28=x27 1.05+200=18400.7379 1.05+20019520.7748 x29=x28 1.05+200=19520.7748 1.05+20020696.8136 x30=x29 1.05+200=20696.8136 1.05+20021931.6543 x31=x30 1.05+200=21931.6543 1.05+20023228.237 x32=x31 1.05+200=23228.237 1.05+20024589.6488 x33=x32 1.05+200=24589.6488 1.05+20026019.1313 x34=x33 1.05+200=26019.1313 1.05+20027520.0878 x35=x34 1.05+200=27520.0878 1.05+20029096.0922 x36=x35 1.05+200=29096.0922 1.05+20030750.8968 x37=x36 1.05+200=30750.8968 1.05+20032488.4417 x38=x37 1.05+200=32488.4417 1.05+20034312.8637 x39=x38 1.05+200=34312.8637 1.05+20036228.5069 x40=x39 1.05+200=36228.5069 1.05+20038239.9323 x41=x40 1.05+200=38239.9323 1.05+20040351.9289 x42=x41 1.05+200=40351.9289 1.05+20042569.5253 n=42



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