The Mathematical Repository Volume 2
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1748 edition. Excerpt: ...of lift; and let the sum ef I I. and its interest for I year, be called the rate. From the lesser complement subtract one, and divide the remainder by fix times the rate j or find this quotient, in table the last. From the value of the life of the oldest person subtract the above found quotient, and multiply the remainder by the lesser complement more one. Divide the last found product by twice the greater complement, and subtract the quotient from the value of the oldest life, then the remainder will be the value of an annuity for the joint lives; which was required. EXAMPLE. What is the value of an annuity of i /. to continue during the joint lives of two persons of the respective ages of 43 and 54) allowing compound interest at sour per Cent, the value of the life of 54 years being 10,478 I Here (86--43=) 43, is the greater complement. And (86--54=) 32, is the lesser complement. Also ( i-f,04=) 1,04 is the rate. Now if (32--1=) 31 be divided by (1,04X6=) 6,24, the quotient will be 4,968. From 10,478, take 4,968, and there will remain 5,510. Which multiplied by (324-1=) 33 will produce 181,830. If the last product 131,830, be divided by (43X2=) S6, the quotient will be 2,114. Which quotient, taken from 10,478, will leave 8,364 for the value of the annuity required. QJJ E S T I O N LXV. What is the present value of an annuity of 1 /. to continue during the joint lives of two persons, each aged 48 years, supposing the decrements of life'to be equal and that compound interest be allowed at 4 per Cent. SOLUTION. The solution of this question may be deduced from that of quest. 64; for if the two complements of life m and a be equal, it will follow that, m-J-n = 2 j tn--it X p--o; and nm--nn Therefore tin value of the annuity will be------l--p x...
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