Question

MUST SHOW ALL WORK (3 pictures)

7. (a) Will the future value be larger or smaller if we compound an initial amount more often than annually-for example, every 6 months, or semiannually - holding the stated interest rate constant? Explain your answer. (2 points)

Answer 1

Q7 a)
Yes the future value be larger if we compound an initial amount more than annually, because in this case the interest is also earning interest every time compounding happens.
b1)
Excel formula	Result
=FV(12%/2,3*2,,-200,0)	$283.70
b2)
APR = 12%
m = 2
EAR = (1+APR/m)^m
=(1+(12%/2))^2-1 = 12.36%
EAR = 12.36%
c1)
APR = 12%
m = 4
Excel formula	Result
=FV(12%/4,3*4,,-200,0)	285.15
c2)
APR = 12%
m = 4
EAR = (1+APR/m)^m
=(1+(12%/4))^4-1 = 12.55%
EAR = 12.55%
d1)
APR = 12%
m = 365
Excel formula	Result
=FV(12%/365,3*365,,-200,0)	286.65
d2)
APR = 12%
m = 365
EAR = (1+APR/m)^m
=(1+(12%/365))^365-1 = 12.75%
EAR = 12.75%