Question

You just found out that you have $5,171.57 in a savings account. Your aunt opened the account in your name exactly 6 years ago, and deposited $X in the account. Then she put in another $752 two years after opening the account. Other than $X and the $752, there were no other deposits. If the interest rate for the past 6 years has been 12%, what is X?  

Answer 1

Solution

The amount put by her after 2 years = 752

Future value= Amount*(1+r)^n

r= rate of interest= 12% in this case

n= number of years

FV of 752 at the end of the sixth year from the day deposit X was made=752*(1+.12)^4

=1183.287

Therefore out of the total amount currently in the account(5171.57),1183.287 has accumulated due to 752 deposit at the end of the second year

Therefore the amount accumulated due to deposit X at the beginning= 5171.57-1183.287 =3988.26

Now we need to find the Present value of 3988.26 discounted @12% for 6 years to get X

PV= Cashflow/(1+r)^n=3988.26/(1+.12)^6

=2020.577

Therefore X=2020.577

If you are satisfied with answer, please give a thumbs up