Question

Derek wants to withdraw $13,149.00 from his account 7.00 years from today and $12,556.00 from his account 15.00 years from today. He currently has $2,480.00 in the account. How much must he deposit each year for the next 15.0 years? Assume a 5.42% interest rate. His account must equal zero by year 15.0 but may be negative prior to that.

Answer 1

Answer: $1,218.48 Per Year.

Calculation:

To calculate this we will start with calculating Present value (PV) of future requirements. Then we will find the value of the annuity which will be equal to the PV in 15 years.

Let's start by calculating the present value of future needs.

PV = Future value / (1+r)ⁿ   Where r = rate = 0.0542, n = period 7 &15, Future value = Future requirement.

After 7 years he wants to withdraw $13,149

So, PV of that amount is 13,149/ (1.0542)^7 = 9087.23255

After 15 years he wants to withdraw $12,556

So, PV of that amount is 12,556/ (1.0542)^7 = 5,688.61

PV of future needs = 9087.2325 + 5688.61 = 14775.84.

However, Currently, he has $2480 in the account. So, he needs...

14775.84 -2480 = 12295.84

He needs PV of $12,295.84 in the form of an annuity till 15 years from now.

PV of annuity = P [ {1- (1+r)^-n} / r]

Where PV of annuity = $12,295.84, P = payment of annuity

r = rate of interest = 0.0542, n= number of year = 15.

Let's put all the values in the equation...

12295.84 = P [ {1- (1+0.0542)^-15} / 0.0542]

12295.84 = P[10.0911612]

So, P = 12295.84/10.0911612

= $1,218.48 Per Year.

If you need more clarification in any step, let me know in the comment section.