Question

You have $ 8000 to invest for 3 years. You have been offered two investment options
Option 1: Invest 9 % p.a. simple interest
Option 2: Invest 8 % p. a compound interest compounded half-yearly
a. Calculate the amount accumulated at the end of 3 years for both options and decide which option to take
b. Would you change your decision if you were investing for 5 years? Explain

Answer 1

Step-by-step explanation:

Simple One-time Interest

I = P0r

A = P0 + I = P0 + P0r = P0(1 + r)

I is the interest

A is the end amount: principal plus interest

P0 is the principal (starting amount)

r is the interest rate (in decimal form. Example: 5% = 0.05)

Answer 2

Step-by-step explanation:

P =$5000, r = 6% , t = 4 years

a) simple : A = P(1+rt)

A = 5000(1+(0.06)(4)) = 5000(1.24) = $6200

b) compounded annually, n = 1:

A = 5000(1 + 0.06/1)(1)(4) = 5000(1.06)(4) = $6312.38

c) compounded semiannually, n =2:

A = 5000(1 + 0.06/2)(2)(4) = 5000(1.03)(8) = $6333.85

d) compounded quarterly, n = 4:

A = 5000(1 + 0.06/4)(4)(4) = 5000(1.015)(16) = $6344.93

e) compounded monthly, n =12:

A = 5000(1 + 0.06/12)(12)(4) = 5000(1.005)(48) = $6352.44

f) compounded daily, n =365:

A = 5000(1 + 0.06/365)(365)(4) = 5000(1.00016)(1460) = $6356.12