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CHAPTER 6-7 - Since your salary grows at 4 percent you...

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Since your salary grows at 4 percent, you deposit will also grow at 4 percent. We can use the present value of a growing perpetuity equation to find the value of your deposits today. Doing so, we find: PV = C {[1/( r g )] – [1/( r g )] × [(1 + g )/(1 + r )] t } PV = $2,600{[1/(.11 – .04)] – [1/(.11 – .04)] × [(1 + .04)/(1 + .11)] 40 } PV = $34,399.45 Now, we can find the future value of this lump sum in 40 years. We find: FV = PV(1 + r ) t FV = $34,366.45(1 + .11) 40 FV = $2,235,994.31 This is the value of your savings in 40 years. 39. The relationship between the PVA and the interest rate is: PVA falls as r increases, and PVA rises as r decreases FVA rises as r increases, and FVA falls as r decreases The present values of $9,000 per year for 10 years at the various interest rates given are: [email protected]% = $9,000{[1 – (1/1.10) 15 ] / .10} = $68,454.72 [email protected]% = $9,000{[1 – (1/1.05) 15 ] / .05} = $93,416.92 [email protected]% = $9,000{[1 – (1/1.15) 15 ] / .15} = $52,626.33 40. Here we are given the FVA, the interest rate, and the amount of the annuity. We need to solve for the number of payments. Using the FVA equation: FVA = $20,000 = $340[{[1 + (.06/12)] t – 1 } / (.06/12)] Solving for t , we get: 1.005 t = 1 + [($20,000)/($340)](.06/12) t = ln 1.294118 / ln 1.005 = 51.69 payments 41. Here we are given the PVA, number of periods, and the amount of the annuity. We need to
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