Question

When Victor is 10 years old, his father deposits a certain amount of money in a university fund that pays 12.4% capitalized semiannually. When Víctor turns 15, his father will deposit an amount equal to the one initially deposited and, when he turns 18, he will start receiving $ 65,000 from the fund each semester, starting at that moment, for 5 years, in order to pay for his career. the value of the 2 deposits.

Answer 1

Let us assume that the value of each deposit be x.

It is given that the deposit is made at the age of 10 and 15. $65,000 will be received at the beginning of each semester for 5 years starting at the age of 18. Rate of interest is 12.4%.

The equation from the given information can be created as:

Future value of two deposits of $x each at age 18 = Present value of $65,000 received at the beginning of each semester at age 18

Future value of deposits = x*(1+12.4/200)^(8*2) + x*(1+12.4/200)^(3*2)

= x*1.062^16 + x*1.062^6

= 2.61813640x + 1.43465376x

= 4.05279016x

Present value of $65,000 received at the beginning of each semester at age 18 can be calculated using annuity due.

Present value of annuity dueof $1 at 12.4% compounded semiannually for 5 years

= (1-(1+12.4/200)^(-5*2))/(12.4/200)*(1+12.4/200)

= 7.74287860

Present Value = $65,000 * 7.74287860 = $503,287.11

Thus, the equation would be

4.05279016x = $503,287.11

x = $124,182.87

Thus, value of each deposit is $124,182.87.