1. Fund A is invested at an effective annual interest rate of 3%. Fund B is invested at an effective annual interest rate of 2.5%
At the end of 20 years, the total in the two funds is 10000. At the end of 31 years, the amount in Fund A is twice the amount in Fund B.
Calculate the total in the two funds at the end of 10 years. Round your answer to the nearest whole number.

2. What nominal annual interest rate compounded monthly is equivalent to an effective annual discount rate of 8% per year for the first 10 years followed by a nominal annual discount rate of 5% compounded daily for the second 10 years?
Note: There are 365 days in a year. Give your answer as a percent rounded to three decimal places.

3. To accumulate 18000 at the end of 7n years, a deposit of 5000 is made at the end of the first 3n years and another deposit of 7200 is made at the end of 5n years.
Find vn where v is taken from our normal actuarial notation and v > 0. Give your answer rounded to three decimal places.

4. You are given two loans, with each loan to be repaid by a single payment in the future. Each payment includes both principal and interest.
The first loan is repaid by a 3000 payment at the end of four years. The interest is accrued at an annual nominal rate of discount equal to 5% compounded semiannually.
The second loan is repaid by a 4000 payment at the end of five years. The interest is accrued at an annual nominal rate of interest equal to 5% compounded quarterly.
These two loans are to be consolidated. The consolidated loan is to be repaid by two equal installments of X, with interest accruing at an annual effective rate of 5%. The first payment is due immediately (i.e. at time t = 0 years), and the second payment is due at the end of the first year (i.e. at time t = 1 year).
Calculate X. Give your answer rounded to the nearest whole number.

5. At a certain interest rate the present value of the following two payment streams are equal:
(i) 200 at the end of 5 years plus 500 at the end of 10 years
(ii) 400.94 at the end of 5 years
At the same interest rate, 100 invested now plus 120 invested at the end of 5 years will accumulate to X at the end of 10 years.
Calculate X. Round your answer to the nearest whole number.

6. Fund F accumulates at a rate of Î´t = 1/1+t, for t > 0
Fund G accumulates at a rate of Î´t = 4t / 1 + 2tÂ², for t > 0

You are given the following pieces of information:
(i) F(t) = Amount in Fund F at time t
(ii) G(t) = Amount in Fund G at time t
(iii) H(t) = F(t) â€“ G(t)
(iv) F(0) = G(0)
(v) T is the time t when H(t) is a maximum.
Calculate T. Give your answer as a decimal rounded to two places.

7. On 01/01/1997, Kelly deposits X into a bank account. The account is credited with simple interest at the rate of 10% per year.
On the same date, Tara deposits X into a different bank account. The account is credited interest using a force of interest, for t being time in years since the investment is made where
Î´t = 2t/(tÂ² + k)
From the end of the 4th year until the end of the 8th year, both accounts earn the same dollar amount of interest. Calculate k. Give your answer rounded to the nearest whole number.

8. Given a nominal annual interest rate of 7.5% convertible every five days, determine the sum of the equivalent:
(i) force of interest; and
(ii) nominal annual discount rate compounded quarterly.
Note: There are 365 days in a year. Give your answer as a decimal rounded to four places.

9. The present value of a payment of 1004 at the end of T months is equal to the sum of the present values of the following payments
(i) 314 at the end of 1 month
(ii) 271 at the end of 18 months
(iii) 419 at the end of 24 months
For all payments, the effective annual interest rate is 5%. Calculate T. Round your answer to the nearest whole number.

10. Bob purchased a promissory note on January 1st, 2009 which agreed to pay simple interest in the amount 8.0% per year. The note will mature and be paid on April 1st, 2009, 90 days later.
Bob sells the note to Sally on February 12th, 2009 (i.e. 42 days after purchasing) for an amount that causes Sallyâ€™s yield rate on the note to be equivalent to simple interest of 6.3% per year.
Sally cashes in the note on April 1st, 2009 for 5000.00. Note: There are 365 days in a year.
What is Bobâ€™s annual yield rate (simple interest) on the note? Give your answer as a percentage rounded to two places. Do not round your calculations, at least not too much, until the very end.

1. Fund A is invested at an effective annual interest rate of 3%. F...