You have your choice of two investment accounts. Investment A is a 7-year annuit
ID: 2772577 • Letter: Y
Question
You have your choice of two investment accounts. Investment A is a 7-year annuity that features end-of-month $1,880 payments and has an interest rate of 10 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 12 percent, also good for 7 years.
How much money would you need to invest in B today for it to be worth as much as Investment A 7 years from now? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
You have your choice of two investment accounts. Investment A is a 7-year annuity that features end-of-month $1,880 payments and has an interest rate of 10 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 12 percent, also good for 7 years.
Explanation / Answer
Solution.
Total amount of investment A is end of 7th year is =
Calculation of investment B
Amount
$2,318,600 would you need to invest in B today for it to be worth as much as Investment A 7 years from now.
Month Deposit Amount Rate Interest Amount 1 $ 1,709.09 10.00% $ 170.91 $ 1,880.00 2 $ 1,880.00 10.00% $ 188.00 $ 2,068.00 3 $ 2,068.00 10.00% $ 206.80 $ 2,274.80 4 $ 2,274.80 10.00% $ 227.48 $ 2,502.28 5 $ 2,502.28 10.00% $ 250.23 $ 2,752.51 6 $ 2,752.51 10.00% $ 275.25 $ 3,027.76 7 $ 3,027.76 10.00% $ 302.78 $ 3,330.53 8 $ 3,330.53 10.00% $ 333.05 $ 3,663.59 9 $ 3,663.59 10.00% $ 366.36 $ 4,029.95 10 $ 4,029.95 10.00% $ 402.99 $ 4,432.94 11 $ 4,432.94 10.00% $ 443.29 $ 4,876.24 12 $ 4,876.24 10.00% $ 487.62 $ 5,363.86 13 $ 5,363.86 10.00% $ 536.39 $ 5,900.25 14 $ 5,900.25 10.00% $ 590.02 $ 6,490.27 15 $ 6,490.27 10.00% $ 649.03 $ 7,139.30 16 $ 7,139.30 10.00% $ 713.93 $ 7,853.23 17 $ 7,853.23 10.00% $ 785.32 $ 8,638.55 18 $ 8,638.55 10.00% $ 863.85 $ 9,502.40 19 $ 9,502.40 10.00% $ 950.24 $ 10,452.65 20 $ 10,452.65 10.00% $ 1,045.26 $ 11,497.91 21 $ 11,497.91 10.00% $ 1,149.79 $ 12,647.70 22 $ 12,647.70 10.00% $ 1,264.77 $ 13,912.47 23 $ 13,912.47 10.00% $ 1,391.25 $ 15,303.72 24 $ 15,303.72 10.00% $ 1,530.37 $ 16,834.09 25 $ 16,834.09 10.00% $ 1,683.41 $ 18,517.50 26 $ 18,517.50 10.00% $ 1,851.75 $ 20,369.25 27 $ 20,369.25 10.00% $ 2,036.92 $ 22,406.17 28 $ 22,406.17 10.00% $ 2,240.62 $ 24,646.79 29 $ 24,646.79 10.00% $ 2,464.68 $ 27,111.47 30 $ 27,111.47 10.00% $ 2,711.15 $ 29,822.62 31 $ 29,822.62 10.00% $ 2,982.26 $ 32,804.88 32 $ 32,804.88 10.00% $ 3,280.49 $ 36,085.37 33 $ 36,085.37 10.00% $ 3,608.54 $ 39,693.90 34 $ 39,693.90 10.00% $ 3,969.39 $ 43,663.29 35 $ 43,663.29 10.00% $ 4,366.33 $ 48,029.62 36 $ 48,029.62 10.00% $ 4,802.96 $ 52,832.58 37 $ 52,832.58 10.00% $ 5,283.26 $ 58,115.84 38 $ 58,115.84 10.00% $ 5,811.58 $ 63,927.43 39 $ 63,927.43 10.00% $ 6,392.74 $ 70,320.17 40 $ 70,320.17 10.00% $ 7,032.02 $ 77,352.19 41 $ 77,352.19 10.00% $ 7,735.22 $ 85,087.40 42 $ 85,087.40 10.00% $ 8,508.74 $ 93,596.15 43 $ 93,596.15 10.00% $ 9,359.61 $ 102,955.76 44 $ 102,955.76 10.00% $ 10,295.58 $ 113,251.34 45 $ 113,251.34 10.00% $ 11,325.13 $ 124,576.47 46 $ 124,576.47 10.00% $ 12,457.65 $ 137,034.12 47 $ 137,034.12 10.00% $ 13,703.41 $ 150,737.53 48 $ 150,737.53 10.00% $ 15,073.75 $ 165,811.28 49 $ 165,811.28 10.00% $ 16,581.13 $ 182,392.41 50 $ 182,392.41 10.00% $ 18,239.24 $ 200,631.65 51 $ 200,631.65 10.00% $ 20,063.17 $ 220,694.82 52 $ 220,694.82 10.00% $ 22,069.48 $ 242,764.30 53 $ 242,764.30 10.00% $ 24,276.43 $ 267,040.73 54 $ 267,040.73 10.00% $ 26,704.07 $ 293,744.80 55 $ 293,744.80 10.00% $ 29,374.48 $ 323,119.28 56 $ 323,119.28 10.00% $ 32,311.93 $ 355,431.21 57 $ 355,431.21 10.00% $ 35,543.12 $ 390,974.33 58 $ 390,974.33 10.00% $ 39,097.43 $ 430,071.76 59 $ 430,071.76 10.00% $ 43,007.18 $ 473,078.94 60 $ 473,078.94 10.00% $ 47,307.89 $ 520,386.83 61 $ 520,386.83 10.00% $ 52,038.68 $ 572,425.51 62 $ 572,425.51 10.00% $ 57,242.55 $ 629,668.06 63 $ 629,668.06 10.00% $ 62,966.81 $ 692,634.87 64 $ 692,634.87 10.00% $ 69,263.49 $ 761,898.36 65 $ 761,898.36 10.00% $ 76,189.84 $ 838,088.19 66 $ 838,088.19 10.00% $ 83,808.82 $ 921,897.01 67 $ 921,897.01 10.00% $ 92,189.70 $ 1,014,086.71 68 $ 1,014,086.71 10.00% $ 101,408.67 $ 1,115,495.39 69 $ 1,115,495.39 10.00% $ 111,549.54 $ 1,227,044.92 70 $ 1,227,044.92 10.00% $ 122,704.49 $ 1,349,749.42 71 $ 1,349,749.42 10.00% $ 134,974.94 $ 1,484,724.36 72 $ 1,484,724.36 10.00% $ 148,472.44 $ 1,633,196.79 73 $ 1,633,196.79 10.00% $ 163,319.68 $ 1,796,516.47 74 $ 1,796,516.47 10.00% $ 179,651.65 $ 1,976,168.12 75 $ 1,976,168.12 10.00% $ 197,616.81 $ 2,173,784.93 76 $ 2,173,784.93 10.00% $ 217,378.49 $ 2,391,163.43 77 $ 2,391,163.43 10.00% $ 239,116.34 $ 2,630,279.77 78 $ 2,630,279.77 10.00% $ 263,027.98 $ 2,893,307.74 79 $ 2,893,307.74 10.00% $ 289,330.77 $ 3,182,638.52 80 $ 3,182,638.52 10.00% $ 318,263.85 $ 3,500,902.37 81 $ 3,500,902.37 10.00% $ 350,090.24 $ 3,850,992.61 82 $ 3,850,992.61 10.00% $ 385,099.26 $ 4,236,091.87 83 $ 4,236,091.87 10.00% $ 423,609.19 $ 4,659,701.06 84 $ 4,659,701.06 10.00% $ 465,970.11 $ 5,125,671.16Related Questions
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