Financial maths question, with method please thanks!

Question

which is the better result at the end of 20 years?

(i) An investment of $100000 at 12% per annum compounded monthly. 

      OR

(ii) $1000 invested monthly at 12% per annum compounded monthly.

Answer 1

The formula for a single investment is simple: FV = PV * (1 + r/n)^nt where PV is the initial investment, rate is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. so you have

 

100,000 (1.01)^240 = FV = 1,089,255

 

A financial calculator or a spreadsheet functions solve this more easily. You input four known variables and solve for the fifth one. The five vaiables are

 

PV = present value of the investment today = 100,000

PMT = the period payment of an annuity  = 0

i% = the interest rate per period = 12%=12 = 1%

N = the number of compounding periods = 240

FV = future value of the investment = ?

 

With a calculator, you input the four known values and press the button for the unknown to get a solution financial calculators are not expensive and they can save a huge amount of time.

 

For the future value of an ordinary annuity, you can look up the formula, which is quite complex and can be tedious to solve. You can use a spreadsheet function to provide the known variables which are

 

PV = 0

PMT = 1,000

i% = 1%

N = 240

FV = ?

 

PV = 999,147.92