Answer to Question #255856 in Economics for Sera

Question

How much is 100,000 pesos worth in three years if deposited in a continuously compounded account with a nominal interest rate of 3%. Determine also its effective rate in one year period compounded; a) daily (on leap year), b) monthly, c) bi-monthly d) quarterly (Note: Answer must be in percentage and in four decimal places.

Answer 1

$A = 100,000×e^{3×0.03} = 109,417.43.$

a) daily (on leap year):

$r = (1 + 0.03/366)^{366} - 1 = 0.030453$

or 3.0453%.

b) monthly:

$r = (1 + 0.03/12)^{12} - 1 = 0.030416$

or 3.0416%.

c) bi-monthly:

$r = (1 + 0.03/6)^{6} - 1 = 0.030378$

or 3.0378%.

d) quarterly:

$r = (1 + 0.03/4)^{4} - 1 = 0.030339$

or 3.0339%.