Question

Mateo has nothing saved for retirement. Mateo wants to receive 30,900 dollars each year for 5 years during retirement. The first of these payments will be received in 6 years. Mateo can earn a return of 4.64 percent per year. How much does Mateo need to save each year for 6 years to have exactly enough to meet his retirement goal if he makes his first savings contribution in 1 year and all savings contributions are equal?

Answer 1

Step 1:

The total present value of the annuity payment of 30900 dollars has to be calculated first, using the following formula (Ordinary Annuity):

P/(1+r)^n

30900/(1+4.64%)^1 +  

30900/(1+4.64%)^2 +  

30900/(1+4.64%)^3 +  

30900/(1+4.64%)^4 +

30900/(1+4.64%)^5 = 135122.69 (Rounded off)

Step 2:

Now, in order to accumulate this amount at the end of 6 years, we need to calculate the annuity payments to be made at the end of every year:

=135122.69/(1+4.64%)^5

=20046.13