Bruce deposits 100 into a bank account. His account is credited interest at an annual nominal rate of interest of 4% convertible semiannually. At the same time, Peter deposits 100 into a separate account. Peter’s account is credited interest at an annual force of interest of δ .After 7.25 years, the value of each account is the same.

Calculate δ .

• 0.0388
• 0.0392
• 0.0396
• 0.0404
• 0.0414

Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of [math]i[/math]. The accumulated amount in the account at the end of 40 years is [math]X[/math], which is 5 times the accumulated amount in the account at the end of 20 years.

Calculate [math]X[/math]

• 4695
• 5070
• 5445
• 5820
• 6195

Eric deposits 100 into a savings account at time 0, which pays interest at an annual nominal rate of [math]i[/math], compounded semiannually. Mike deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of [math]i[/math]. Eric and Mike earn the same amount of interest during the last 6 months of the 8th year.

Calculate [math]i[/math].

• 9.06%
• 9.26%
• 9.46%
• 9.66%
• 9.86%

Jeff deposits 10 into a fund today and 20 fifteen years later. Interest for the first 10 years is credited at a nominal discount rate of d compounded quarterly, and thereafter at a nominal interest rate of 6% compounded semiannually. The accumulated balance in the fund at the end of 30 years is 100.

Calculate d.

• 4.33%
• 4.43%
• 4.53%
• 4.63%
• 4.73%

Ernie makes deposits of 100 at time 0, and X at time 3. The fund grows at a force of interest

The amount of interest earned from time 3 to time 6 is also X

Calculate X.

• 385
• 485
• 585
• 685
• 785

David can receive one of the following two payment streams:

• 100 at time 0, 200 at time n years, and 300 at time 2n years
• 600 at time 10 years

At an annual effective interest rate of i, the present values of the two streams are equal.

Given 0.76 = vⁿ, calculate i

• 3.5%
• 4.0%
• 4.5%
• 5.0%
• 5.5%

Payments are made to an account at a continuous rate of [math]8k + tk[/math], where [math]0 \leq t \leq 10.[/math]

Interest is credited at a force of interest [math] \delta_t = \frac{1}{8 + t}.[/math]

After time 10, the account is worth 20,000.

Calculate k.

• 111
• 116
• 121
• 126
• 131

Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Each account earns the same annual effective interest rate.

The amount of interest earned in Bruce's account during the 11th year is equal to X. The amount of interest earned in Robbie's account during the 17th year is also equal to X.

Calculate X.

• 28.00
• 31.30
• 34.60
• 36.70
• 38.90

An investor pays 100,000 today for a 4-year investment that returns cash flows of 60,000 at the end of each of years 3 and 4. The cash flows can be reinvested at 4.0% per annum effective.

Using an annual effective interest rate of 5.0%, calculate the net present value of this investment today.

• –1,398
• –699
• 699
• 1,398
• 2,629

The annual force of interest credited to a savings account is defined by

with [math]t[/math] in years. Austin deposits 500 into this account at time 0.

Calculate the time in years it will take for the fund to be worth 2000.

• 6.7
• 8.8
• 14.2
• 16.5
• 18.9