Deposits of 100 are made to an account today and one year from today. The annual force of interest at time t in years for this account is:

Calculate the account balance two years from today.

• 211.07
• 211.87
• 216.05
• 216.79
• 220.24

John deposits 1000 into a fund. The fund earns:

1. an annual nominal rate of interest of 4% convertible quarterly for the first three years;
2. a constant annual force of interest of 5% for the next three years; and
3. an annual nominal discount rate of 6% convertible semiannually thereafter.

Calculate the amount in the fund at the end of ten years.

• 1658
• 1667
• 1670
• 1674
• 1677

A store purchased couch #1 for X two months ago and plans to sell it for 1500 six months from today. The same store purchases couch #2 for X today and plans to sell it for 1500 four months from today. The annual force of interest is a constant 10%. The current value of the store’s cash flows from the purchase and sale of couch #2 is 260.

Calculate the current value of the store’s cash flows from the purchase and sale of couch #1.

• 216
• 218
• 256
• 260
• 307

The annual force of interest is [math]\delta_t=\frac{2}{10-t}[/math], for [math]0 \leq t\lt10[/math], in which [math]t[/math] is measured in years.

Calculate the equivalent annual nominal discount rate compounded every two years for the period [math]2.0 \leq t \leq 2.4[/math].

• 1,758
• 1,828
• 1,901
• 2,078
• 2,262

At a force of interest [math]\delta_t=\frac{0.5}{5+0.5 t}, 0 \leq t \leq 6[/math] an investment of 1000 at time [math]t=2[/math] will accumulate to [math]X[/math] at time [math]t=6[/math]. At an annual nominal rate of discount of [math]8 \%[/math] convertible quarterly, an investment of [math]Y[/math] will accumulate to [math]X[/math] at the end of two years.

• 1124
• 1129
• 1134
• 1138
• 1143

A retailer offers two payment plans:

1. A 2% discount if paid within 10 calendar days after purchase
2. Pay the full amount on the 30th day after purchase

Assume a 365-day year.

The implied annual effective yield the buyer is charged for delaying payment from day 1 to day 30 is i.

Calculate i.

• 24.3%
• 26.8%
• 27.9%
• 36.5%
• 44.6%

You are given that the force of interest at time t (in years) is [math]\frac{1}{t+8}[/math]

Calculate the annual effective rate of interest in year 5.

• 6.2%
• 6.6%
• 7.4%
• 8.3%
• 9.5%

John deposits money into an account that has a payment of $25,000 at the end of 5 years. Sally deposits money into 2 accounts. One has a payment of 4,000 at the end of year t and one has a payment of $17, 000 at the end of year 2t. The sum of Sally’s present value is equal to John’s present value and is equal to a deposit with payment of $7,000 at time 0.

Find the value of the payment $14,000 at the end of year t+4 if all interest rates are equal for all deposits.

• $2,704
• $3,894
• $58,956
• $26,737
• $3,498,106

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Eric deposits $6,000 into an account that gives 6% interest annually. He takes out $2,000 at the end of years 7, 14, and 21 at a penalty of 4%. What is the accumulated value of the deposit at the end of year 23?

• $16,678.50
• $5,507.16
• $11,783.36
• $8,695.22
• $35,053.63

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Michael deposits $20,000 into his bank account. For the first 4 years the bank credits an interest of i convertible quarterly and 3i convertible monthly after that.

If he has $80,000 in his account after 14 years, how much does he have after 3 years?

• $26,918.25
• $22,084.93
• $22,873.49
• $22,604.63
• $22,603.53

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.