Question

Grov morsqucrat w sporada to trobracabat agrob) noituso to jo 1992 anilo to natura 4. Cindy has set up an ordinary annuity to save for her retirement in 30 years. If the monthly be payments are $400 and the annual rate of interest is 8.25% compounded monthly, what will the value of the annuity be when she retires ? OS tog Vino on lo vb za riboining to to sign bror SAT) Sbsting frolar o una woh anionin ob srl ni llindart to TED ( 0010 nodrog to slillon S Ta borudo sa bobol woolmio ob slenterar o apoi wo 288,01 to obtatnio BTT tool om att Os es SCHOO

Answer 1

The monthly rate of intenest is = 8.21% = 0.006875 First de posit = $400; It future value affen 30 years that is 30x12 months is = 400(1+0.006(75) 3 60 400(1.006875736 3Go 359 The second deposit is a month late; it has only 359 months to grow and its fininal value is 400/1.00 6675) In similar way, we find We found that the last deposit has just one month to earn interest. putting it all together, we have S = 400 (1.006875) 360 * Soo (1.006875) ti 4400(1.0068753354 This is geometric series with first terom (a) = 400 (1.006875) 400 (1.006875) 360 and common Ratio (P) = 1 7.006875 360 1 400(1.006875 i. Final value = ( I- (19006875736) & 1.006875 ) (+- a (1-son) [ Sna 2 "}] 1-p = 631.600.20.2 .. the value of the annuity be when she nebines is 631600.202