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1.An insurance company promotes a ten-year life insurance with zero cost. In the scheme,$10000 is deposited by the insurer on the same insurance date of the year for ten years.After ten years, a total of $100000 is returned to the insurer.Assume that the interest rate is 4%p.a.,which is compounded annually.Find the... 顯示更多 1.An insurance company promotes a ten-year life insurance with zero cost. In the scheme,$10000 is deposited by the insurer on the same insurance date of the year for ten years.After ten years, a total of $100000 is returned to the insurer.Assume that the interest rate is 4%p.a.,which is compounded annually.Find the actual cost to the nearest dollar of the life insurance policy. 更新: 2.The sum to infinity of an infinite geometric sequence is 16 and the sum to infinity of the squares of its terms is 153.6 . Find the common ratio and the fourth term of the sequence.
最佳解答:
1. a = first term r = common ratio GP sum = a [ (r^n) –1 ] / (r-1) a = 10000 r = 1.04 GP sum = 10000 [ (1.04^10) – 1] / (1.04 – 1) = 120061 (to the nearest dollar) Therefore actual cost is 120061 – 100000 = $20061 2. GP sum to infinity = a / (1 – r) The sum to infinity of an infinite geometric sequence is 16 means: a / (1 – r) = 16 a = 16(1-r) The sum to infinity of the squares of its terms is 153.6 means: a would become a^2 r would become r^2 a^2 / (1 – r^2) = 153.6 256 ( 1 – 2r + r^2 ) = 153.6 – 153.6 r^2 256 – 512r + 256r^2 = 153.6 – 153.6r^2 409.6r^2 – 512r + 102.4 = 0 4r^2 – 5r +1 = 0 r = 1/4 or 1 (rejected because r cannot be 1 or otherwise the 分母would equal to 0 ) a = 12 4th term is 12 x (1/4)^3 = 3/16
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F5 math problems ( Summing a sequence )發問:
1.An insurance company promotes a ten-year life insurance with zero cost. In the scheme,$10000 is deposited by the insurer on the same insurance date of the year for ten years.After ten years, a total of $100000 is returned to the insurer.Assume that the interest rate is 4%p.a.,which is compounded annually.Find the... 顯示更多 1.An insurance company promotes a ten-year life insurance with zero cost. In the scheme,$10000 is deposited by the insurer on the same insurance date of the year for ten years.After ten years, a total of $100000 is returned to the insurer.Assume that the interest rate is 4%p.a.,which is compounded annually.Find the actual cost to the nearest dollar of the life insurance policy. 更新: 2.The sum to infinity of an infinite geometric sequence is 16 and the sum to infinity of the squares of its terms is 153.6 . Find the common ratio and the fourth term of the sequence.
最佳解答:
1. a = first term r = common ratio GP sum = a [ (r^n) –1 ] / (r-1) a = 10000 r = 1.04 GP sum = 10000 [ (1.04^10) – 1] / (1.04 – 1) = 120061 (to the nearest dollar) Therefore actual cost is 120061 – 100000 = $20061 2. GP sum to infinity = a / (1 – r) The sum to infinity of an infinite geometric sequence is 16 means: a / (1 – r) = 16 a = 16(1-r) The sum to infinity of the squares of its terms is 153.6 means: a would become a^2 r would become r^2 a^2 / (1 – r^2) = 153.6 256 ( 1 – 2r + r^2 ) = 153.6 – 153.6 r^2 256 – 512r + 256r^2 = 153.6 – 153.6r^2 409.6r^2 – 512r + 102.4 = 0 4r^2 – 5r +1 = 0 r = 1/4 or 1 (rejected because r cannot be 1 or otherwise the 分母would equal to 0 ) a = 12 4th term is 12 x (1/4)^3 = 3/16
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