Fifteen years ago, you deposited $12,500 into an investment fund. Five years ago, you added an additional $20,000 to that account. You earned 8%, compounded semi-annually, for the first ten years, and 6.5%, compounded annually, for the last five years. Required: a) What is the effective annual interest rate (EAR) you would get for your investment in the first 10 years? b) How much money do you have in your account today? c) If you wish to have $85,000 now, how much should you have invested 15 years ago?

The answer to the question are (a) The EAR = 8.160 (b) The Amount for $12500 for 10 years compounded semi annually  si = $ 22,700 , and The  Amount for $32,500 for 5 Years compounded annually = $ 43,062.50 (c) $65,762.50

Step-by-step explanation:

Solution

The Initial deposit is = $12,500

Additional investment  for five years = $20,000

Interest for compounded semi annually for first 10 years = 8%  

Interest compounded annually for last five years =6.5%

Now,

(a) The EAR will be = [1+ interest nominal rate/number of compounding periods)]^ no. of compounding periods-1

The EAR = 8.160

(b) The Amount for $12500 for 10 years compounded semi annually  si = $ 22,700 , and The  Amount for $32,500 for 5 Years compounded annually = $ 43,062.50

(c) Let say that  amount be X

Now,

For first 10 years at= 8.160 %

Thus,

The  Amount of interest = ( X * 8.160% * 10 ) = 0.8160 X

IN 5 years  time, the Interest Amount = (X * 6.5% * 5) = 0.325 X

At the end of 15 Years,the Total money  = 85000

Which is,

0.8160X + 0.3250X + X = 85000

Therefore,

X = $ 39,700

The Money in today account is  = $65,762.50

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step-by-step explanation: