$50,000 is invested in such a way as to repay the investor an interest payment o
ID: 2773894 • Letter: #
Question
$50,000 is invested in such a way as to repay the investor an interest payment of $1,000 at the end of each quarter for 10 years. At the end of the 10 years, the $50,000 is returned in a lump sum.As soon as he interest payment is received, it is deposited in a savings account bearing interest at 6% nominal annual rate compounded quarterly. It is desired to find the nominal rate of return, compounded semiannually, on the $50,000 investment over the 10 year period. Which of the following expresses the rate of return?
A. 2.085/10, B. 2.085/20, C. ((2.085)^(1/10))-1, D ((2.085)^(1/20))-1, E. 2((2.085)^(1/20))-1
Please, no excel spreadsheets.
Explanation / Answer
Initial investment USD 50,000 Cash received at end of 10 years from initial investment USD 50,000 The USD 1000 invested quarterly represents annuity, compounted quarterly at nominal rate of return of 1.50% (i) for a tenor of 40 (n) quarters Future value of annuity = quarterly payment * [ {(1+i)^n-1}/(i)] Future value of annuity = 1000 * [ {(1+1.50%)^40-1}/(1.50%)] 54267.89 Total cash at the end of 10 years = USD (50,000+54,267.89) USD 104,267.89 We need arrive at nomian rate of return compounded annually (y) (Cash at the end of 10 year/Initial investment = (1+y)^20 (1+y)^20 =2.085 y = {2.085^(1/20)} - 1 Answer is option D
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