Question

If money is invested for 10 years, the per annum simple interest rate equivalent to a nominal rate of 6.5%p.a compounding quarterly is

Answer 1

The concept used in the solution is compound rate of interest and simple rate of interest.

Solution :

Let us assume $ 1000 invested today at 6.5 % compunded quaterly

Step 1 : Value after 10 years at compound interest

Future value = Investment amount * Future value interest factor (peroidic rate r, n period)

                    = 1000 * FVIF ( 6.5% / 4 , 10 years * 4)

                   = 1000 * FVIF (1.625%, 40 period)

                   = 1000 * (1.01625)40

                   = 1000 * 1.905559

                   = $ 1905.56

Step 2 : Return under compound interest in 10 years

Returns = Future value - Initial investment

              = 1905.56 - 1000

              = $ 905.56

Return per year = Returns / years

                         = 905.56 / 10 years

                         = 90.556

Step 3 : Equivalent rate of simple interest

Rate = Returns per year under compound interest / Investment * 100

        = [ 90.556 / 1000 ] * 100

        = 9.0556 % or 9.06% per annum (Approx) Answer

Hope you understand the solution.