B. You are offered $900 five years from mow or $150 at the end of each year for
ID: 2636992 • Letter: B
Question
B. You are offered $900 five years from mow or $150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept? If you can earn 14 percent on your funds, which offer will you accept? Why are your answers different? 9. The following questions illustrate nonannual compounding. a) one hundred dollars is placed in an account that pays 12 percent. How much will be in the account after one year if Interest is compounded annually, semiannually, or monthly? b) One hundred dollars Is to be received after one year. What is the present value of this amount If you can earn 12 percent compounded annually, semiannually, or monthly? 10. At the end of each year, Tom invests $2,000 In a retirement account. Joan also invests $2,000 in a retirement account but makes her deposits at the beginning of each year. They both earn 9 percent on their funds. Flow much will each have in his or her account at the end of 20 years? 11. You purchase a $100,000 life insurance policy for a single payment of $35,000. If you want to earn 9 percent on invested funds, how soon must you die for the policy to have been the superior alternative? If you die within ten years, what is the return on the investment In life insurance? (Morbid questions, but you might want to view life insurance as an investment alternative. As one financial planner told the author: Always look at the numbers; analyze life insurance as an investment)Explanation / Answer
Answer:- 8
option A- receive $ 900 now (beginning of the year)
option B- receive $ 150 end of every year at the rate of 6% for 5 years
calculation of future value of annuity = present value {(1 +r)n - 1) / r}
future value of annuity = 150 {(1 + 0.06)5 - 1) / 0.06}
future value of annuity = $ 845.56
Future value of annuity at the rate of 14% for 5 years
= 150 {(1 + 0.14)5 - 1) / 0.14}
= $ 991.51
so accecpt the 14% propasal, because we earn $ 991.51 instead of $ 900
Answer: 9
a) principle - $100, interest rate - 12%, year 1
compounded annuallly
A = 100 (1 +12%)1
A = $ 112
compounded semi-annually, then the interest rate will divide by 2 = 12% / 2 = 6%, and year will multiply by 2 - 1year * 2 = 2 year
A = $ 100 (1+6%)2
A = $ 112
compounded quaterly, then interest rate divide by 4 = 12% / 4 = 3% and the year will multiply by 4 - 1year * 4 = 4 year
A = $ 100 (1+3%)4
A = $ 112
every time answer will be same.
b) future value = $ 100, rate of interest = 12%, year= 1 (annuilty formula)
Annually compounding =
Present vlue of annuity = FV / {(1 - (1+r)n ) / r }
Present value of annuity = 100 * 0.89 = $ 89.28
present value of annuity(semi-annully)- rate of interest will go to 6% (12% / 2) and year will be 2 years
present value of annuity = $ 88.99
present value of annuity (monthly) = rate of interest is 1% and year will be 12 year
present value of annuity = $ 88.74
answer is same
answer : 10
tom deposit $ 2000 at the end of every year, for 20 year at 9 %
so, the tom deposit of last 20th year, will not received any interest on that, because it is at end of the year. so future value of annuity is:-
future value of annuity = present value {(1 +r)n - 1) / r}
= 2000 {( 1+0.09)19 - 1) / 0.09}
= 2000 * 50.16 = $ 100,320 and add $2000 (last year)
= $ 102,320
joan deposit is beginning of the year = 2000 {( 1+0.09)20 - 1) / 0.09}
= $ 2000 * 54.67 = $ 109,349
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