Question

Bart is a junior in college. He plans to invest equal, annual amounts starting 5 years from now for 7 consecutive years in order to accumulate a total of $49,000 at the end of 15 years. If the funds earn 8% per year, what is the required amount of each deposit?

Answer 1

Bart plans to Invest equal annual payments starting 5 years frm now for 7 consecutive years and accumulate $49,000 at the end of year 15.

first, we will calculate the Present Value at the end of year 12 of the accumulated value:-

Present Value = Future Accumulated Value/(1+r)^n

where, r = interest rate = 8%

n = No of years = 3

Present Value = $49,000/(1+0.08)^3

= $49,000/1.259712

= $38,897.78

Now the value at the end of year 12 is $38,897.78

Now, we will use teh value at the end of year 12 to compute the periodic equal installments:-

Where, C= Periodic Payments

r = Periodic Interest rate = 8%

n= no of periods = 7

C =$4036.45

So, the required amount of each deposit is $4036.45