Question

Instead of investing the entire $1,050,800, Bogut invests $282,200 today and plans to make 8 equal annual investments into the fund beginning one year from today. What amount should the payments be if Bogut plans to establish the $2,601,739 foundation at the end of 8 years?

Answer 1

Bogut must calculate the future value of the initial investment and then determine the annual payments using the future value of annuity formula, considering the difference needed to reach the total $2,601,739 in 8 years.

Step-by-step explanation:

The question asks how much Bogut should invest annually to achieve a $2,601,739 foundation in 8 years, given an initial investment of $282,200. To solve this problem, one would typically use the formulas for future value of a single sum and future value of an annuity in the context of compound interest.

First, the future value of the initial investment needs to be calculated. Thereafter, the future value that the annuity payments need to reach (minus the future value of the initial investment) should be calculated using the future value of annuity formula. Once these calculations are completed, Bogut will know the amount to be invested annually for 7 years to achieve the goal.

Answer 2

Annual deposit= $195,494.90

Step-by-step explanation:

Giving the following information:

Bogut invests $282,200 today and plans to make 8 equal annual investments into the fund beginning one year from today.

Final value= $2,601,739

We need to calculate the final value of the first investment (282,200), and then calculate the 8 equal deposits.

To determine the final value, we need the interest rate. I will invent an interest rate 0f 8% compounded annually.

FV=PV*(1+i)^n

FV= 282,200*(1.08^8)= $522,332.50

Difference= 2,601,739 - 522,332.50= $2,079,406.5

To calculate the annual deposit, we will use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (2,079,406.5*0.08)/ [(1.08^8)-1]= $195,494.90