Compound interest

Question

1500 dollars is invested for 18 months at a nominal rate of 13%. Find the accumulated value if interest is compounded (i) monthly (ii) continuously.

Answer 1

The formula for compound interest non-continuously is:

A = P (1+ (r/n))^nt

Where:

A = the final amount

P=Principal

r= rate

t=number in years

n=number of times the money is compounded in a year.

e.g. compunded monthly means n=12

P=1500

r=13%=0.13

t= 1.5 (18 months = 1.5 years)

(i) n=12

Solve for A:

A=1500(1 + (0.13/12))^12*1.5

A=1500(1.010833...)¹⁸

A=$1821.06

(ii) For continuously the formula is:

A=Pe^rt

e = is the Euler's number, is a mathematical constant approximately equal to 2.71828

A=1500e^0.13*1.5

A=$1822.97