suppose you can invest 1000 in a fund earning simple discoun

suppose you can invest $1000 in a fund earning simple discount at an annual rate of 8% or in a fund earning simple interest at an annual rate of 12%. How long must you invest your money in order for the simple discount account to be preferable?

Solution

If we invest $1000 today at a simple interest rate of 12%, then after 1 year,

we will have $1000 *(1+0.12) = $1120

If we invest $1000 in a fund earning simple discount at an annual rate of 8%, then after 1 year,

we will have $1000 *(1/1.08)^1 = $926

If we invest $1000 in a fund earning simple discount at an annual rate of 8%, then after 1 year,

we will have $1000 *(1/1.08)^2 = $857

We must invest $1000 for 2 years in order for the simple discount account to be preferable as after 2 years the returns would be $1783.