標題:
MATHS_Indices and Iogarithms
發問:
In the compound interest () formula A = P (1 + R)^a, (a) if P = 100,000 , r = 8%, n = 5, find the value of A, (b) if A = 21,003.42, P = 10,000 , n = 5 , find the valiue of r , (c) if A = 80957.13, P = 35000, r = 15%, find the value of n. 更新: In the compound interest (複利息) formula A = P (1 + R)^a,
In the compound interest () formula A = P (1 + R)^a, (a) if P = 100,000 , r = 8%, n = 5, find the value of A, Ans: A = P (1 + R)^a=100,000 (1+8%)^5=146932.8// (b) if A = 21,003.42, P = 10,000 , n = 5 , find the valiue of r , Ans: A = P (1 + R)^a 21,003.42=10000(1+R)^5 2.100042 = (1+R)^5 => log 2.100042 = 5 log (1+R) => log(1+R)=0.64445596 =>1+R=1.159966898 =>R=16%// (c) if A = 80957.13, P = 35000, r = 15%, find the value of n. Ans: A = P (1 + R)^a 80957.13=35000(1+15%)^n =>2.095713=(1+0.15)^n =>log 2.095713 = n log 1.15 => n = log 2.095713 / log 1.15 =5.3 //
其他解答:
SOLUTIONS : (a) When P = 100,000 , r = 8% and n = 5, A = 100,000 (1 + 8%)^5 = 100000 (1.08)^5 = 146932.8077 = 147000 (b) When A = 21,003.42, P = 10,000 and n = 5, 21003.42 = 10000( 1 + r )^5 2.100042 = ( 1 + r )^5 (2.100042)^ 1 / 5 - 1 = r r = 0.159966898 = 15.996698 % = 16.0 % (c) When A = 80957.13, P = 35000 and r = 15%, 80957.13 = 35000( 1 + 15% )^n 80957.13 / 35000 = ( 1.15 )^n log80957.13 / 35000 = nlog1.15 n = log80957.13 / 35000 / log 1.15 = 6.000000283 = 6.00 ALL ANSWERS ARE CORRECT TO 3 SIG. FIG. 2009-04-04 01:17:32 補充： n = (log80957.13 / 35000) / (log 1.15) this form will be better rather than 'n = log80957.13 / 35000 / log 1.15' 2009-04-04 03:46:39 補充： (a) A = $ 147000
MATHS_Indices and Iogarithms
發問:
In the compound interest () formula A = P (1 + R)^a, (a) if P = 100,000 , r = 8%, n = 5, find the value of A, (b) if A = 21,003.42, P = 10,000 , n = 5 , find the valiue of r , (c) if A = 80957.13, P = 35000, r = 15%, find the value of n. 更新: In the compound interest (複利息) formula A = P (1 + R)^a,
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最佳解答:In the compound interest () formula A = P (1 + R)^a, (a) if P = 100,000 , r = 8%, n = 5, find the value of A, Ans: A = P (1 + R)^a=100,000 (1+8%)^5=146932.8// (b) if A = 21,003.42, P = 10,000 , n = 5 , find the valiue of r , Ans: A = P (1 + R)^a 21,003.42=10000(1+R)^5 2.100042 = (1+R)^5 => log 2.100042 = 5 log (1+R) => log(1+R)=0.64445596 =>1+R=1.159966898 =>R=16%// (c) if A = 80957.13, P = 35000, r = 15%, find the value of n. Ans: A = P (1 + R)^a 80957.13=35000(1+15%)^n =>2.095713=(1+0.15)^n =>log 2.095713 = n log 1.15 => n = log 2.095713 / log 1.15 =5.3 //
其他解答:
SOLUTIONS : (a) When P = 100,000 , r = 8% and n = 5, A = 100,000 (1 + 8%)^5 = 100000 (1.08)^5 = 146932.8077 = 147000 (b) When A = 21,003.42, P = 10,000 and n = 5, 21003.42 = 10000( 1 + r )^5 2.100042 = ( 1 + r )^5 (2.100042)^ 1 / 5 - 1 = r r = 0.159966898 = 15.996698 % = 16.0 % (c) When A = 80957.13, P = 35000 and r = 15%, 80957.13 = 35000( 1 + 15% )^n 80957.13 / 35000 = ( 1.15 )^n log80957.13 / 35000 = nlog1.15 n = log80957.13 / 35000 / log 1.15 = 6.000000283 = 6.00 ALL ANSWERS ARE CORRECT TO 3 SIG. FIG. 2009-04-04 01:17:32 補充： n = (log80957.13 / 35000) / (log 1.15) this form will be better rather than 'n = log80957.13 / 35000 / log 1.15' 2009-04-04 03:46:39 補充： (a) A = $ 147000
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