Question

8) Find the value of $1000 invested in an account (2.5, 3.1, 3.2)
a. Bearing 3 % simple interest after 5 years.
b. Bearing 3 % interest compounded monthly after 5 years.
c.Bearing 3 % interest compounded continuously after 5 years.

Answer 1

ANSWER:

A) Simple interest:

i = 3% , principal = $1,000 and n = 5 years

simple interest for 5 years = i * p * n = 3% * 1,000 * 5 = $150

value of account after 5 years = principal + simple interest for 5 years = $1,000 + $150 = $1,150

B) monthly compounding:

i = 3% per year or 3% / 12 = 0.25% per month

n = 5 years or 5 * 12 = 60 months

fv = pv * (1 + i) ^ n

fv = 1,000 * (1 + 0.25%) ^ 60

fv = 1,000 * (1.0025) ^ 60

fv = 1,000 * 1.161617

fv = 1,161.61

so the future value after 5 years is $1,161.61

C) Continous compounding:

i = 3% per year

n = 5 years

Fv = pv * e ^ in

fv = 1,000 * 2.7183 ^ 3% * 5

fv = 1,000 * 1.161835

fv = 1,161.835

so the future value is $1,161.83