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 Math Central Quandaries & Queries
 Question from rose, a student: Darnell wants to have 2700$to purchase a tv in 20 months. what will he need to deposit today if he earns 5% annual interest compounded monthly Hi Rose, If the annual interest rate is$5\% = 0.05$then the monthly interest rate is$\frac{0.05}{12} = 0.004166667.$Thus if Darnell deposits$X$dollars today then in one month its value will be $X + 0.004166667 \times X = 1.004166667 \times X \mbox{ dollars. }$ This amount is then invested for one month at a monthly rate of 0.004166667 per month so at the end of the second month Darnell will have $1.004166667 \times X + 1.00416667 \times X = 1.00416667^2 \times X \mbox{ dollars.}$ This amount is then invested for one month at a rate of 0.00416667 per month. How much will Darnell have at the end of the third month? How much will Darnell have at the end of the twentieth month? Set this equal to 2700 dollars and solve for$X.\$

Penny

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