SOA EXAM FM SAMPLE QUESTIONS
WITH CORRECT ANSWERS
5.
An association had a fund balance of 75 on January 1 and 60 on December 31. At the
end of every month during the year, the association deposited 10 from membership
fees. There were withdrawals of 5 on February 28, 25 on June 30, 80 on October 15,
and 35 on October 31.
Calculate the dollar-weighted (money-weighted) rate of return for the year. - Correct
Answers -(E) 11.0%
7.
1000 is deposited into Fund X, which earns an annual effective rate of 6%. At the end of
each year, the interest earned plus an additional 100 is withdrawn from the fund. At the
end of the tenth year, the fund is depleted.
The annual withdrawals of interest and principal are deposited into Fund Y, which earns
an annual effective rate of 9%.
Calculate the accumulated value of Fund Y at the end of year 10. - Correct Answers -
(C) 2085
45.
You are given the following information about an investment account:
(i) The value on January 1 is 10.
(ii) The value on July 1, prior to a deposit being made, is 12.
(iii) On July 1, a deposit of X is made.
(iv) The value on December 31 is X.
Over the year, the time-weighted return is 0%, and the dollar-weighted (money-
weighted) return is Y.
Calculate Y. - Correct Answers -(A) -25%
15.
A 10-year loan of 2000 is to be repaid with payments at the end of each year. It can be
repaid under the following two options:
(i) Equal annual payments at an annual effective interest rate of 8.07%.
(ii) Installments of 200 each year plus interest on the unpaid balance at an annual
effective interest rate of i.
The sum of the payments under option (i) equals the sum of the payments under option
(ii).
Calculate i. - Correct Answers -(B) 9.00%
, 16.
A loan is amortized over five years with monthly payments at an annual nominal interest
rate of 9% compounded monthly. The first payment is 1000 and is to be paid one month
from the date of the loan. Each succeeding monthly payment will be 2% lower than the
prior payment.
Calculate the outstanding loan balance immediately after the 40th payment is made.
(A) 6750 (B) 6890 (C) 6940 (D) 7030 (E) 7340 - Correct Answers -(B) 6890
106.
A company takes out a loan of 15,000,000 at an annual effective discount rate of 5.5%.
You are given:
i) The loan is to be repaid with n annual payments of 1,200,000 plus a drop payment
one year after the nth payment.
ii) The first payment is due three years after the loan is taken out.
Calculate the amount of the drop payment.
(A) 79,100
(B) 176,000
(C) 321,300
(D) 959,500
(E) 1,180,300 - Correct Answers -(D) 959,500
24.
A 20-year loan of 20,000 may be repaid under the following two methods:
(i) amortization method with equal annual payments at an annual effective interest rate
of 6.5%
(ii) sinking fund method in which the lender receives an annual effective interest rate of
8% and the sinking fund earns an annual effective interest rate of j
Both methods require a payment of X to be made at the end of each year for 20 years.
Calculate j.
(A) 6.4%
(B) 7.6%
(C) 8.8%
(D) 11.2%
(E) 14.2% - Correct Answers -(E) 14.2%
26.
Seth, Janice, and Lori each borrow 5000 for five years at an annual nominal interest
rate of 12%, compounded semi-annually.
Seth has interest accumulated over the five years and pays all the interest and principal
in a lump sum at the end of five years.
Janice pays interest at the end of every six-month period as it accrues and the principal
at the end of five years.
Lori repays her loan with 10 level payments at the end of every six-month period.
Calculate the total amount of interest paid on all three loans.
(A) 8718
WITH CORRECT ANSWERS
5.
An association had a fund balance of 75 on January 1 and 60 on December 31. At the
end of every month during the year, the association deposited 10 from membership
fees. There were withdrawals of 5 on February 28, 25 on June 30, 80 on October 15,
and 35 on October 31.
Calculate the dollar-weighted (money-weighted) rate of return for the year. - Correct
Answers -(E) 11.0%
7.
1000 is deposited into Fund X, which earns an annual effective rate of 6%. At the end of
each year, the interest earned plus an additional 100 is withdrawn from the fund. At the
end of the tenth year, the fund is depleted.
The annual withdrawals of interest and principal are deposited into Fund Y, which earns
an annual effective rate of 9%.
Calculate the accumulated value of Fund Y at the end of year 10. - Correct Answers -
(C) 2085
45.
You are given the following information about an investment account:
(i) The value on January 1 is 10.
(ii) The value on July 1, prior to a deposit being made, is 12.
(iii) On July 1, a deposit of X is made.
(iv) The value on December 31 is X.
Over the year, the time-weighted return is 0%, and the dollar-weighted (money-
weighted) return is Y.
Calculate Y. - Correct Answers -(A) -25%
15.
A 10-year loan of 2000 is to be repaid with payments at the end of each year. It can be
repaid under the following two options:
(i) Equal annual payments at an annual effective interest rate of 8.07%.
(ii) Installments of 200 each year plus interest on the unpaid balance at an annual
effective interest rate of i.
The sum of the payments under option (i) equals the sum of the payments under option
(ii).
Calculate i. - Correct Answers -(B) 9.00%
, 16.
A loan is amortized over five years with monthly payments at an annual nominal interest
rate of 9% compounded monthly. The first payment is 1000 and is to be paid one month
from the date of the loan. Each succeeding monthly payment will be 2% lower than the
prior payment.
Calculate the outstanding loan balance immediately after the 40th payment is made.
(A) 6750 (B) 6890 (C) 6940 (D) 7030 (E) 7340 - Correct Answers -(B) 6890
106.
A company takes out a loan of 15,000,000 at an annual effective discount rate of 5.5%.
You are given:
i) The loan is to be repaid with n annual payments of 1,200,000 plus a drop payment
one year after the nth payment.
ii) The first payment is due three years after the loan is taken out.
Calculate the amount of the drop payment.
(A) 79,100
(B) 176,000
(C) 321,300
(D) 959,500
(E) 1,180,300 - Correct Answers -(D) 959,500
24.
A 20-year loan of 20,000 may be repaid under the following two methods:
(i) amortization method with equal annual payments at an annual effective interest rate
of 6.5%
(ii) sinking fund method in which the lender receives an annual effective interest rate of
8% and the sinking fund earns an annual effective interest rate of j
Both methods require a payment of X to be made at the end of each year for 20 years.
Calculate j.
(A) 6.4%
(B) 7.6%
(C) 8.8%
(D) 11.2%
(E) 14.2% - Correct Answers -(E) 14.2%
26.
Seth, Janice, and Lori each borrow 5000 for five years at an annual nominal interest
rate of 12%, compounded semi-annually.
Seth has interest accumulated over the five years and pays all the interest and principal
in a lump sum at the end of five years.
Janice pays interest at the end of every six-month period as it accrues and the principal
at the end of five years.
Lori repays her loan with 10 level payments at the end of every six-month period.
Calculate the total amount of interest paid on all three loans.
(A) 8718
