13©8 
THE RURAL NEW-YORKER 
December 0, 
THE INSURANCE PROBLEM. 
On page 115S the Hope Farm man told 
of a man who 20 years ago took out a 
life insurance policy for $3,000. He paid 
$80 every six months and at the end of 
the 20 years received $3,991.74. Here 
are three problems stated by the Hope 
Farm man. The following answers have 
been submitted : 
“1. I understand this company loans 
money on an average of about five per 
cent. This being so, what has this man’s 
money been worth to the company—paid 
in $80 each six months or 40 payments 
in all? 2. Suppose this man had put $80 
each six months in a savings bank at 
four per cent instead of taking the in¬ 
surance, how much would he have now? 
3. Suppose he had taken a simple death 
policy for about $60 per year and banked 
$100 each year at four per cent, what 
would he have now?” 
Problem No. 1 
Interest 5 per cent or 2)4 per cent in 6 months 
1+.035=1.026. 
Log. 1.025 =0.01072 
40 
T Log. (1.0251 40 =0.42880=Log. of 2.684. 
2.681 — 1=1.684=a mount of semiannuity of 
.025 in 20 years. 
.025=^j, hence 1.684 x 40=67.30=amount of 
semiannuity of SI.00, interest as above stated. 
67.36 x 80=$5,388.80. A nswer. 
Problem No. 2. 
Interest=4 per cent=2 per cent in 6 months. 
Log. 1.02 =0.00860 
_40 
Log. (1,02) 4 ° =0.344ii0=Log. of 2.208, 2.208—1 = 
1.208=amount of semiannuity of .02 in 20 years. 
.02 = X hence 1.208 x 50 = $60.40 = amount of 
eemiannuity of SI.00. 
60.40 x 80=§4,832.00. Answer. 
Problem No. 3. 
Interest = 4 per cent. 
Log. 1.04 = 0.01703 
_20 
Log. (1.04)20 = 0.34060 = Log. 2.191 
2.191—1=1.191 amount of annuity of .04 in 20 
years. 
1.191 x 25 = 29.775=amount of annuity of $ 1 - 00 . 
29.775 x 100=S2,977.50=amount of annuity of 
$100. 
Answer—$ 2 , 077.50 in bank and policy for $3,000 
at the end of the 20th year. 
New York. frank l. teal. 
Following are the answers to “insur¬ 
ance,” on page 1158: 
1. Allowing the first payment to be at the 
end of the first six months, we have as total 
interest and payments: 
(ras? n@“+n ®°>= * m ] Lg^- 1 1 = 
$5,392.32. The value of =—is found by loga- 
1.025 
rithms, thus— 
40- log- 1.025 = 40- .010724 = .428960 
Hence t^ 40 =S2.6851. 
1.02a 
2 " $8 ° (ro2 30+ rd2 !t8+1 ) =$4 ' 832 - 02 - 
3. $50 ( + j )= $3,020.01 (Besides life 
insurance.) 
4. Question: What rate was actually paid? 
Thus solve for x : 
( _ 40 ) 
*80 J l+x—1 > =3991.74, an equation of the 
I - f 40th degree and has 40 roots, 
' x ' what are they ? 
See whether .01099 is not the required root, 
thus making the rate actually 2.198 per cent 
compounded semiannually. 
WALTER L. BROWN. 
Orleans Co., N. Y. 
You raise the question of whether a 
certain man received fair treatment from 
a life insurance company in the case of 
a 20-year endowment policy for $3,000. 
Undoubtedly he did. His $160 a year 
for 20 years totaled $3,200. The com¬ 
pany offered to pay him practically $4,- 
000, or 25% more than he had paid in. 
Being paid in annual instalments over 
20 years, the company had the equivalent 
of $1,600 for 20 years, or $3,200 for 
10 years, and paid him 2*4 % interest 
on $3,200 for each of 10 years. A sav¬ 
ings bank would have paid him 4% a 
year. The difference of 1 *4% ^'^s the 
cost to him of the protection which he 
received, out of which the company must 
pay his share of death losses and his 
share of agency and general expenses. 
Spread over 20 years that cost to him 
was only $24 per year on the $3,000, or 
$8 per year for each $1,000. 
It is not a question of what the com¬ 
pany could earn from the use of his 
money, because out of those earnings 
actual death losses and current expenses 
must be paid. Although an insurance 
company can loan out some of its funds 
at 5% and 6%, it is impossible to keep 
the average up to that. Most insurance 
rates are figured on a supposed basis of 
earnings of 3*4% to 4%. 
True, had he put $160 each year in a 
savings bank at 4%, or had he taken 
a straight life policy at a lower premium 
rate and put the difference in the hank, 
he would have been worth more money 
if he lived out the 20 years, but (1st) 
he would not have had the insurance 
protection in the one case, nor would his 
premiums have ceased at the end of the 
20 years in the other case, and (2nd) he 
probably would not have had the will 
power to carry out this investment plan 
to the end. F. J. batchelder. 
New York. 
On page 1158 you inquire concerning 
the life insurance policy for $3,000 at 
semi-annual payments of $80 for 20 years, 
or a total cost of $3,200, and showing 
at end of the time a cash value of $3,- 
991.74. The soliciting agent may, at 
times, overstate some benefits to accrue 
from a policy, in his zeal to induce his 
prospect to do his duty in that line with¬ 
out further procrastination; for the agent 
must be an optimist to succeed. He be¬ 
lieves that most men will insure at some 
period and he knows the uncertainty of 
life and good health. 
He knows also that his company is 
safer than any bank; more stable, in 
fact, than any form of property for so 
long a period, or a lifetime, perhaps, 
yes, more stable than a government bond, 
for they fluctuate and depend upon the 
life of a nation, under its present form. 
Your inquiry is of an endowment at 
age of about 32 years. The insured paid 
the company $3,200 and received for it 
$3,991.74, besides being insured for the 
full 20 years for $3,000, to be paid in 
cash to his beneficiary should he die at 
any time after paying even oqe premium. 
Term insurance would have cost him 
$46 a year, instead of $160 that was 
paid for this endowment, leaving 8114 
to deposit in the savings bank, which in 
20 years at 4 per cent would amount to 
$3,534 or $457.74 less than he now re¬ 
ceives. 
A whole life rate, non-participating 
policy, would have cost him $63 a year, 
leaving $97 to deposit, which would 
amount to $3,007.00; and policy cash 
value of $841, making a total of $3,S48, 
or $143.74 less than the endowment value. 
A 20-payment life, non-participating 
policy, would have cost $88 per year, 
leaving $72 to deposit each year which 
would amount to $2,232, compounded. at 
four per cent annually; plus a pAicy 
cash value of $1,593.00, or total 
of $3,S25, or $166.74 less than the en¬ 
dowment. 
Of each 1,000 men of his age 162 died, 
and their beneficiaries received $3,000 
each, during the period of 20 years, if 
insured for the same amount as the policy 
being discussed. A 11 agent likes to sell 
endowment policies to young m'en who 
desire a property on paper that can be 
carried in their pockets, and that can 
be used as collateral for temporary loans, 
or for long time loans from the company, 
at a low rate of interest, payable at their 
own convenience during the life of the 
policy. 
Endowments promote thrift and savings 
from many who would draw money out 
of a bank "for speculating in the get-rich- 
quick schemes, or for unprofitable ex¬ 
penses in pursuit of pleasure. The pride 
of owning a gun. horse and dog is often 
transferred to the insurance policy for 
the mother, the wife, or the child, and 
a youth who pays his premiums on good 
insurance is a future financier. 
Pennsylvania. J. c. frencii. 
Taking up the second section of your 
question I find: Present savings bank 
value of $S0 deposited semi-annually at 
4 per cent interest compounded semi¬ 
annually, $4,928.11. Present value of his 
policy, $3,991.74. Net cost of $3,000 in¬ 
surance for 20 years, $937.37. Net cost 
per year. $46.86. Net cost per thousand 
per year, $15.62. 
I should call insurance at $15.62 per 
thousand per year very reasonable in¬ 
surance. Third section of question.— 
Present value of policy, $3,991.74. 
$1,100 deposited $50 semi-annually at 
4 per cent compounded interest, 20 years 
value, $3,081.09. Present value of 
straight policy nothing, if you are alive 
and there are no dividends due and no 
surrender value, making advantage of en¬ 
dowment policy by difference, $910.75. 
Taking it another way, $60, his pay¬ 
ments on straight life, deposited $30 in 
bank semi-annually at four per cent com¬ 
pounded interest making net cost of 
straight policy for 20 years $1,847.10. 
Net cost for $3,000 per year, $92.35. Net 
cost per thousand per year, $30.78. Net 
cost nearly twice that of the endowment. 
Of course the actual cost is $60 per year 
or $20 per thousand, but there are usual¬ 
ly some dividends which make the eost 
practically the same in either policy. As 
a fact the life policy has a value in that 
it is continued at a lower rate than a 
new policy can be taken when 20 years 
advanced in age. 
I am not an insurance expert, and my 
way of figuring may not be right, but I 
have figured on a number of different 
forms of policies and the insurance act¬ 
ually cost practically the same in them 
all. The endowment policies seem to 
give you insurance at the regular rate 
and about four per cent on your money, 
and offer the advantage that you have 
to save a certain amount and cannot 
as readily draw it out to squander it on 
new automobiles or other fancied necessi¬ 
ties as you can if it is in the bank. 
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