Question

An engincering college want to create a $68,443 trust fund for course textbooks each semester during the regular school (two times a year). If the fund has a 3% nominal interest rate compounded blannually, how much must be in the fund to start to keep it going indefinitely?

Answer 1

The engineering college needs to deposit a principal of $4,562,866.67 to create a perpetuity that can provide $68,443 twice a year at a 3% interest rate compounded semiannually.

Step-by-step explanation:

The question pertains to the calculation of the initial principal needed to create a perpetuity, which is a type of annuity that lasts indefinitely. A perpetuity formula derived from the compound interest formula is used to calculate the principal. In this scenario, the engineering college seeks to establish a trust fund that can indefinitely provide $68,443 twice a year (semiannually) at a nominal interest rate of 3% compounded semiannually. To find the required principal (P), we use the perpetuity formula P = A / r, where A is the semiannual withdrawal of $68,443 and r is the semiannual interest rate (1.5% or 0.015). Therefore, the principal P needed is P = $68,443 / 0.015, which equals $4,562,866.67.