### CFA Practice Question

There are 410 practice questions for this study session.

### CFA Practice Question

Which of the following amounts is closest to the end value of investing \$80,000 for 3 years compounded continuously at a rate of 12%?

A. \$112,750
B. \$113,550
C. \$114,667

EAR = (er - 1) = e.12 - 1 = 0.1275 (12.75%)
End value after 3 years = 80,000 (1 + 0.1275)3 = \$114,667.31

User Comment
brimann BAII+ Solution .12 continuously compounded = 1.1275 I/Y = 12.75 (1.1275-1) N = 3 PV = -80,000 PMT = 0 FV = 114,667
KD101 Can someone try it for me using Brimann's method, I am getting 116,922.4145
jaan Briman's method,
EFF=12.7497 (ie calculated above) C/Y = 12 e^log =162754.7914 ENTER
CPT NOM = 12.00
Note (C/Y = 12 because countinuously compounding period is 12 months)
jimmymh an easier way would be just, .12*3 then 2nd e^x, times 80,000
PeterW2006 With continuous compounding, at any time t, the value of a deposit is given by
ae^(rt)
For this question,
a = 80,000
e = 2.71828
r = 12% continuous compounding rate
t = 3 years

Value = 80,000 x e^(0.12x3)
= 114,666.33
cptp Can somebody explain 12.75%?
Indira EAR=(1+per.int.rate)^m - 1
EAR=(1+0.12/365)^365-1=0.1275
mansi for continous compounding the formula is (e^r-1)
on substituting r=12, you will get 12.75
o123 ICONV ; NOM=12, C/Y=365 --->EFF= 12.74746
mordja do yourselves a favour and use jimmymh's method.
JKiro An add on to jimmymh's method:-
For an interest that is compounded continuously, the formula to be memorized:
FV=PV*e^(r*N) or PV=FV/e^(r*N)
where r = rate; N = number of years
seankang hp 12c
1)1enter, 0.12ge* equals 1.1275
2)n3,12.75i,pv80,000,fv114,667
SANTOSHPRABHU Using BA II Plus:
As rate is = 12% = 0.12
EAR (Continuously compounded) = (0.12 ex - 1) = 1.1275 -1 = 0.1275 = 12.75% = I/Y
N = 3
PV= - 80,000
FV = \$114,667.
rhardin Just make your Number of periods equal 3 x 365 (which is 1,095) in your calculator so there is compounding everyday, and you will still come up with the right answer without having to memorize the formula for continous compounding. Make your I=.12/365 and solve for FV. And you're done!
jansen1979 Great comment by rhardin. Works really easy this way.
8thlegend The question is getting to me. Because we are in the subject of ordinary annuity or annuity due.

Isn't the question saying that he or she is investing 80k every year for 3 years?
Struggler Effective Interest Rate = (1+Periodic Interest Rate)^number of periods in a year

then - 1

Shout out to ma boy rhardin!
johntan1979 If you don't round (by right you should NOT), it's 114,659.57
birdperson jimmymh knows whats up
plammar71 Put pmt