Lucas opens a bank account with 1000 and lets it accumulate at an annual nominal interest rate of 6% convertible semiannually. Danielle also opens a bank account with 1000 at the same time as Lucas, but it grows at an annual nominal interest rate of 3% convertible monthly. For each account, interest is credited only at the end of each interest conversion period.

Calculate the number of months required for the amount in Lucas’s account to be at least double the amount in Danielle’s account.

• 276
• 282
• 285
• 286
• 288

Bill and Joe each put 10 into separate accounts at time t = 0, where t is measured in years. Bill’s account earns interest at a constant annual effective interest rate of K/25, K > 0.

Joe’s account earns interest at a force of interest, [math]\delta_t = \frac{1}{K + 0.25t}[/math]

At the end of four years, the amount in each account is X.

Calculate X.

• 20.7
• 21.7
• 22.7
• 23.7
• 24.7

An investor wishes to accumulate 5000 in a fund at the end of 15 years. To accomplish this, she plans to make equal deposits of X at the end of each year for the first ten years. The fund earns an annual effective rate of 6% during the first ten years and 5% for the next five years.

Calculate X.

• 224
• 284
• 297
• 312
• 379

A couple decides to save money for their child's first year college tuition. The parents will deposit 1700 n months from today and another 3400 2n months from today. All deposits earn interest at a nominal annual rate of 7.2%, compounded monthly.

Calculate the maximum integral value of n such that the parents will have accumulated at least 6500 five years from today.

• 11
• 12
• 18
• 24
• 25

Let S be the accumulated value of 1000 invested for two years at a nominal annual rate of discount d convertible semiannually, which is equivalent to an annual effective interest rate of i.

Let T be the accumulated value of 1000 invested for one year at a nominal annual rate of discount d convertible quarterly.

[math]S/T = (39/38)^4.[/math]

Calculate [math]i[/math]

• 10.0%
• 10.3%
• 10.8%
• 10.9%
• 11.1%

At time 0, Cheryl deposits X into a bank account that credits interest at an annual effective rate of 7%. At time 3, Gomer deposits 1000 into a different bank account that credits simple interest at an annual rate of y%. At time 5, the annual forces of interest on the two accounts are equal, and Gomer’s account has accumulated to Z.

Calculate Z.

• 1160
• 1200
• 1390
• 1400
• 1510

Bank P offers a 3-year certificate of deposit that pays an annual effective interest rate of 4%. In addition, a bonus of 2% of the initial investment is paid at the end of the 3-year period. Bank Q offers a 3-year certificate of deposit without any bonus.

Calculate the annual effective interest rate that Bank Q would have to offer to produce the same annual yield as the certificate from Bank P.

• 4.3%
• 4.4%
• 4.5%
• 4.6%
• 4.7%

An investor deposits 100 into a bank account at time 0. The bank credits interest at an annual nominal interest rate of i, compounded semi-annually. The total amount of interest credited in the twelfth year is twice the amount of interest credited in the fifth year.

Calculate i.

• 10.15%
• 10.24%
• 10.32%
• 10.41%
• 10.48%

Fund X receives a deposit of 1000 at time 0. Fund X accumulates at a nominal rate of interest k, compounded semiannually.

Fund Y receives a deposit of 921.90 at time 0. Fund Y accumulates at a nominal rate of discount, also equal to k, compounded semiannually. At the end of 5 years, the accumulated amount in Fund X and the accumulated amount in Fund Y are both equal to P.

Calculate P.

• 1820
• 1970
• 2100
• 2240
• 2370

A corporation makes a payment at the end of each month into a savings account that offers an annual nominal interest rate of 8% compounded quarterly.

Determine the equivalent effective rate of interest per payment period.

• (1 + 8%/4)^1/3-1
• (1 + 8%/12)-1
• (1 + 8%/12)³-1
• (1 + 8%/12)^1/12-1
• (1 + 8%/4)⁴-1