Find the present-value equivalent to the following geometrically increasing seri
ID: 1168962 • Letter: F
Question
Find the present-value equivalent to the following geometrically increasing series of payments.
(PLEASE show work starting with formula used.)
a. A first-year base of $4,000 increasing at 4% per year to year 15 at an interest rate of 17% compounded continuously. Answer: $23,659
b. A first-year base of $100 increasing at 10% per year to year 12 at an interest rate of 6% compounded continuously.
c. A first-year base of $7,000 increasing at 7% per year to year 20 at an interest rate of 19% compounded continuously.
Explanation / Answer
A. 17% year increase base interest compounded base interest rate interest 1 - 4,000.00 - 4,000.00 17% 680.00 2 4% 4,160.00 680.00 4,840.00 17% 822.80 3 4% 4,326.40 822.80 5,149.20 17% 875.36 4 4% 4,499.46 875.36 5,374.82 17% 913.72 5 4% 4,679.43 913.72 5,593.15 17% 950.84 6 4% 4,866.61 950.84 5,817.45 17% 988.97 7 4% 5,061.28 988.97 6,050.24 17% 1,028.54 8 4% 5,263.73 1,028.54 6,292.27 17% 1,069.69 9 4% 5,474.28 1,069.69 6,543.96 17% 1,112.47 10 4% 5,693.25 1,112.47 6,805.72 17% 1,156.97 11 4% 5,920.98 1,156.97 7,077.95 17% 1,203.25 12 4% 6,157.82 1,203.25 7,361.07 17% 1,251.38 13 4% 6,404.13 1,251.38 7,655.51 17% 1,301.44 14 4% 6,660.29 1,301.44 7,961.73 17% 1,353.49 15 4% 6,926.71 1,353.49 8,280.20 17% 1,407.63 Total 16,116.56 Total interest + Principal=16,116.56+ 6926.71 23,043.27 Present value equivalent to above geometrically increasing series of payment is $ 23,043.27 B. 6% year increase base interest compounded base interest rate interest 1 - 100.00 - 100.00 6% 6.00 2 10% 110.00 6.00 116.00 6% 6.96 3 10% 121.00 6.96 127.96 6% 7.68 4 10% 133.10 7.68 140.78 6% 8.45 5 10% 146.41 8.45 154.86 6% 9.29 6 10% 161.05 9.29 170.34 6% 10.22 7 10% 177.16 10.22 187.38 6% 11.24 8 10% 194.87 11.24 206.11 6% 12.37 9 10% 214.36 12.37 226.73 6% 13.60 10 10% 235.79 13.60 249.40 6% 14.96 11 10% 259.37 14.96 274.34 6% 16.46 12 10% 285.31 16.46 301.77 6% 18.11 Total 135.34 Total interest + Principal=135.34+285.31 420.65 Present value equivalent to above geometrically increasing series of payment is $ 420.65 C. 19% year increase base interest compounded base interest rate interest 1 - 7,000.00 - 7,000.00 19% 1,330.00 2 7% 7,490.00 1,330.00 8,820.00 19% 1,675.80 3 7% 8,014.30 1,675.80 9,690.10 19% 1,841.12 4 7% 8,575.30 1,841.12 10,416.42 19% 1,979.12 5 7% 9,175.57 1,979.12 11,154.69 19% 2,119.39 6 7% 9,817.86 2,119.39 11,937.25 19% 2,268.08 7 7% 10,505.11 2,268.08 12,773.19 19% 2,426.91 8 7% 11,240.47 2,426.91 13,667.38 19% 2,596.80 9 7% 12,027.30 2,596.80 14,624.10 19% 2,778.58 10 7% 12,869.21 2,778.58 15,647.79 19% 2,973.08 11 7% 13,770.06 2,973.08 16,743.14 19% 3,181.20 12 7% 14,733.96 3,181.20 17,915.16 19% 3,403.88 13 7% 15,765.34 3,403.88 19,169.22 19% 3,642.15 14 7% 16,868.92 3,642.15 20,511.07 19% 3,897.10 15 7% 18,049.74 3,897.10 21,946.84 19% 4,169.90 16 7% 19,313.22 4,169.90 23,483.12 19% 4,461.79 17 7% 20,665.15 4,461.79 25,126.94 19% 4,774.12 18 7% 22,111.71 4,774.12 26,885.82 19% 5,108.31 19 7% 23,659.53 5,108.31 28,767.83 19% 5,465.89 20 7% 25,315.69 5,465.89 30,781.58 19% 5,848.50 Total 65,941.72 Total interest + Principal=65941.72+ 25315.69 91,257.41 Present value equivalent to above geometrically increasing series of payment is $ 91,257.41
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