A dlepesit fx maale into a fund which Pays an annual nterest

A dlepesit fx maale into a fund which Pays an annual nterest o 6 At the same tine X is leposited n h ngoin tor lo years At the some time X is leposited into a tund whch Ps an annual effective of dcoun op o Gnaintr o ears The ame unt of interest earned over or mount of interest fr both Punds is euol Cacuiate d tun Fund 2 StartX Stort: X 2 end x C1.06) -10 interest, x (1,06)-x 10 2 6-4)-1\"-25 g/695

Solution

Discount rate d means instead of paying full principal of x/2 for n years it is sufficient to pay the amount so that future value is x/2

Or Future value = P(1+d)¹⁰ = x/2

Hence P = x/2 (1+d)^-10

If both interest equal, then

x(1.06)¹⁰-x = x/2 (1+d)^-10 -x/2

Cancel x

1.06¹⁰-1 = (1+d)^-10-1/2

Solving d = -0.0905 = -9.05%

Since d is discount, we get negative value

So discount rate is 9.05%