3. The average American has $91 lying about. Stick $91 in an ordinary annuity ac

Question

3. The average American has $91 lying about. Stick $91 in an ordinary annuity account each year for 12 years at 4% interest compounded annually and watch it grow. What is the cash value of this annuity at the end of year 12? 4, Jennifer invests $2,400 at the end of each year for 11 years in an ordinary annuity at 10% interest compounded annually. What is the final value of Jennifer's investment at the end of year 11? 5. At the beginning of each period for 11 years, Bobby Nelson invests $470 semiannually at 4%, com year 11? pounded semiannually. What is the cash value of this annuity due at the end of

Explanation / Answer

3. Formula:

Future Value of an ordinary annuity: FV = Pmt x ((1+r)n -1))/r)

Where: Pmt is deposit per period, r is interest rate per period and n is number of periods.

Payment per period (PMT) = $91
Interest Rate per period = 4%
Number of periods (n) = 12 Years

FV = $91 x ((1+0.04)12 -1))/0.04)
=> $91 x (0.601032219/0.04)
=> $91 x 15.02580546 = $1,367.35

4. Payment per period (PMT) = $2,400
Interest Rate per period = 10%
Number of periods (n) = 11 Years

FV = $2,400 x ((1+0.10)11 -1))/0.10)
=> $2,400 x (1.853116706/0.10)
=> $2,400 x 18.53116706 = $44,474.80

5. Formula:

Future Value of an ordinary annuity: FV = Pmt x ((1+r)n -1))/r) x (1+r)

Payment per period (PMT) = $470
Interest Rate per period = 4%/2 = 2%
Number of periods (n) = 11 x 2 = 22 Years

FV = $470 x ((1+0.02)22 -1))/0.02) x (1.02)
=> $470 x (0.545979671/0.02) x (1.02)
=> $470 x 27.29898354 x1.02 = $13,087.13

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