Question

A person deposits 7000 in a bank account. Three years later, he withdraws 5000.
Two years after that, he withdraws an additional 3000. One year after that, he deposits an additional 4000. If interest is 6% compounded annually and that no other deposits or withdrawals are made, how much in his account, 10 years after initial deposits?
(a) 9586 (b) 6053 (c) 3000 (d) none

Answer 1

To solve this problem, let's break it down into several steps.

Step 1: Calculate the value after 3 years
Using the compound interest formula, we can find the value after 3 years:
A = P(1+r)^n
Where:
A = value after n years
P = principal amount (initial deposit)
r = interest rate (6% or 0.06)
n = number of years (3)

A = 7000(1+0.06)^3
A = 7000(1.06)^3
A = 7000(1.191016)
A = 8347.11

Step 2: Calculate the value after 5 years
To find the value after 5 years, we need to subtract the first withdrawal of $5000:
Value after 5 years = 8347.11 - 5000
Value after 5 years = 3347.11

Step 3: Calculate the value after 7 years
To find the value after 7 years, we need to subtract the second withdrawal of $3000:
Value after 7 years = 3347.11 - 3000
Value after 7 years = 347.11

Step 4: Calculate the value after 8 years
To find the value after 8 years, we need to add the additional deposit of $4000:
Value after 8 years = 347.11 + 4000
Value after 8 years = 4347.11

Step 5: Calculate the value after 10 years
Using the compound interest formula again, we can find the value after 10 years:
A = 4347.11(1+0.06)^2
A = 4347.11(1.06)^2
A = 4347.11(1.1236)
A = 4887.24

Therefore, the person has $4887.24 in their account 10 years after the initial deposit.

So, the correct answer is (d) none.