Payments are made to an account at a continuous rate of [math]100e^{0.5t}[/math] from time t = 1 to time t = 3. The force of interest for this account is [math]\delta = 8\%[/math].

Calculate the value of the account at time t = 4.

• 313
• 432
• 477
• 606
• 657

An investor deposited 1000 in each of Bank X and Bank Y. Bank X credits simple interest at an annual rate of 10% for the first five years and 7% thereafter. Bank Y credits interest at an annual nominal rate of 5% compounded quarterly. The interest credited in the eighth year by Bank Y exceeds the interest credited in the eighth year by Bank X by N.

• 0.36
• 2.14
• 20.00
• 56.36
• 56.93

The amount that must be invested at i% (0% < i% < 10%) to accumulate to Y at the end of three years at an annual rate of:

i) simple interest of i% is Q

ii) compound interest of i% is R

iii) simple discount of i% is S

iv) compound discount of i% is T

Determine which of the following is true.

• Q < R < S < T
• R < Q < S < T
• S < T < R < Q
• T < S < Q < R
• T < S < R < Q

Fund [math]\mathrm{X}[/math] accumulates at a force of interest of [math]\delta_t=\frac{2}{1+2 t}[/math], where [math]t[/math] is measured in years, [math]0 \leq t \leq 20[/math]. Fund [math]\mathrm{Y}[/math] accumulates at an annual effective interest rate of [math]i[/math]. An amount of 1 is invested in each fund at time [math]t=0[/math]. After 20 years, Fund X has the same value as Fund [math]\mathrm{Y}[/math].

Calculate the value of Fund Y after five years.

• 2.46
• 2.53
• 2.60
• 2.67
• 2.74

The total present value of 10,000 now and 10,815 two years from now is the same as the present value of 20,800 one year from now at either of two different annual effective interest rates, x and y.

Calculate the absolute value of the difference between x and y.

• 1.8%
• 2.0%
• 3.0%
• 4.0%
• 5.0%

The total present value of 10,000 now and 10,815 two years from now is the same as the present value of 20,800 one year from now at either of two different annual effective interest rates, x and y.

Calculate the absolute value of the difference between x and y.

• 1.8%
• 2.0%
• 3.0%
• 4.0%
• 5.0%

Paul makes one investment of 500 on January 1, 2005 and collects 600 on January 1, 2007 for an annual effective yield of X%. Toby invests 100 on January 1, 2005, invests another 100 on January 1, 2006, and collects an amount Z on January 1, 2007 for an annual effective yield of Y%.

The combination of Paul’s and Toby’s cash flows, produces an annual effective yield of 10%.

Calculate Y% −X%

• 0%
• 1%
• 2%
• 3%
• 4%

A ten-year certificate of deposit pays an annual effective interest rate of 8%. If the balance is withdrawn before the end of ten years, the purchaser can choose between two different penalties:

1. a loss of the last nine months’ interest.
2. a reduction in the annual effective rate of interest to j.

If the purchaser withdraws the funds after three years, the two penalties are equivalent.

Calculate j

• 5.74%
• 5.94%
• 6.14%
• 6.34%
• 6.54%

An investor deposits 150 today and receives 100 one year from now and 80 two years from now. Calculate the annual nominal rate of interest convertible quarterly that the investor earns.

• 12.8%
• 13.0%
• 13.2%
• 13.4%
• 13.6%

Two deposits are made into a fund: 300 at time 0 and X at time 4. The force of interest for the fund is [math]\delta_t = t/50, \, t \geq 0 [/math]. The amount of interest earned from time 0 to time 10 is 4X.

Calculate X .

• 145
• 173
• 181
• 192
• 201