On January 1, 2000, $10, 450 was deposited into an account that earns 5.82% inte

Question

On January 1, 2000, $10, 450 was deposited into an account that earns 5.82% interest compounded monthly. On January 1, 2008, $1, 500 was withdrawn from the account and the bank changed the interest rate to 4.75% compounded monthly. On January 1, 2011, $2, 050 was deposited into the account and the interest rate was lowered to 3.42% compounded monthly. Do the following: A. If no other deposits, withdrawals, or rate changes occur, how much money did the account have on January 1, 2016? Use appropriate formulas to help you solve this problem; do riot use the TVM Solver. Show all the steps needed to solve this problem. B. Determine the total interest that was earned from January 1, 2013 to January 1, 2016? Use appropriate formulas to help you solve this problem; do not use the TVM Solver. Show how you arrived at your answer.

Explanation / Answer

$10,450 amount was deposited in the account for 8 years at the rate of 5.82% per annum.

Using compounding formula
P = 10450
n = 8 *12 = 96 months
r = 5.82 / 12 = 0.485 per month

Amount = 10450 * (1 + 0.485/100)^96 = $16627.81

Now, $1500 was withdrawn,
$16627.81 - $1500 = 15127.81 left in the account.

New, interest rate = 4.75% per annum = 4.75/12 = 0.3958% per month.
hence at the end of 2010 amount will become
15127.81 * (1 + 0.3958/100)^36 = 17439.57

On January 1, 2011, $2050 deposited and new interest rate will be 3.42%

17439.57 + 2050 = 19489.57
Amount on January 1, 2016 will be
19489.57 * (1 + 0.285/100)^60 = 23118.57

(B)
On January 1, 2013, amount present in account will be 19489.57 * (1 + 0.285/100)^24 = 20867.28

amount present in the account on January 1, 2016 is 23118.57.

Hence interest earned is 23118.57 - 20867.28 = $2251.29
  

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