Mark wants to withdraw $6,500 at the end of three years and $8,000 at the end of five years. He wants to do this in such a way that the account balance drops to zero after the last withdrawal. Assuming that the interest rate is 5%, how much money should Mark deposit today to ensure that his needs are met?

Question

10-08-2017
Mathematics

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Mark wants to withdraw $6,500 at the end of three years and $8,000 at the end of five years. He wants to do this in such a way that the account balance drops to zero after the last withdrawal. Assuming that the interest rate is 5%, how much money should Mark deposit today to ensure that his needs are met?

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Aliwohaish12 Aliwohaish12 · Answer 1 · 2017-08-10T20:31:44+02:00

The formula is
P=A÷(1+r)^t
A the last withdrawal is 8000
P the remaining amount 2 years ago?
R interest rate 0.05
T time 2 years
P=8,000÷(1+0.05)^(2)
p=7,256.2358276644 this is the remaining balance that mark invested after drawing the amount of 6500

Add the withdrawal amount of 6500 to the remaining balance to get
7,256.2358276644+6,500
=13,756.235827664

Now use the formula again to find the amount invested 5 years ago
P=A÷(1+r)^t
p=13,756.235827664÷(1+0.05)^(3)
p=11,883.15....answer