Non Annual Compounding It is now January 1. You plan to make a total of 5 deposi

Question

Non Annual Compounding

It is now January 1. You plan to make a total of 5 deposits of $300 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 10% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. How much will be in your account after 10 years? Round your answer to the nearest cent.
$   

You must make a payment of $1,845.06 in 10 years. To get the money for this payment, you will make 5 equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 6% with quarterly compounding. How large must each of the 5 payments be? Round your answer to the nearest cent.
$  

Explanation / Answer

Part 1

As the compounding is done semi-annually, therefore the total periods would be 2*10years = 20periods and the effectaive rate of interest would be 10%/2 = 5%

Now, as per the question

Total money after 10years = $300*(1+5%)20 + $300*(1+5%)19 + $300*(1+5%)18 + $300*(1+5%)17 + $300*(1+5%)16

   = $3,618.53 ~ $3,619

The bank account will have $3,619 after 10years.

Part 2

As the compounding is done quarterly, therefore the total periods would be 4*10years = 40periods and the effectaive rate of interest would be 6%/4 = 1.5%

Also let each of the equal quaterly payments be P.

Therefore, as per the question

$1,845.06 = P*(1+1.5%)40 + P*(1+1.5%)39 + P*(1+1.5%)38 + P*(1+1.5%)37 + P*(1+1.5%)36

=> $1,845.06 = 8.81*P

=> P = $209.52 ~ $210

The 5 equal quarterly payments should be $210 each.

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