Original practice · fully worked
Original variant: first common credit date after two accounts cross
Account A starts with 1,000 and earns 6% nominal interest convertible semiannually. Account B starts with 990 and earns 6.2% nominal interest convertible monthly. Values are compared only on dates when both accounts credit interest. Find the first comparison date, in months, when B is at least as large as A.
- A
36 months - B
42 months - C
48 months - D
54 months - E
60 months
Answer and calculation
The continuous crossing is at 3.691 years; the next common credit date is 48 months. The first qualifying comparison date is 48 months, which is choice C.
Setup
Setup
Convert each nominal quote to its annual accumulation factor and solve the value equality in continuous time.
gA=(1.03)2=1.06090000,gB=(1+0.062/12)12=1.06379253 Model
Model
Because comparisons occur only at dates common to monthly and semiannual crediting, round the crossing time up to the next half-year.
990gBt≥1000gAt Compute
Compute
The continuous crossing is at 3.691 years; the next common credit date is 48 months.
t≥ln(gB/gA)ln(1000/990)=3.6912 years Answer
Answer
The first qualifying comparison date is 48 months, which is choice C.
6⌈2t⌉=48 months(C) 