A father set aside money for his 8 year old daughter\'s future education, by mak

Question

A father set aside money for his 8 year old daughter's future education, by making monthly deposits to bank account that pays 6% per year compounded annually. What equal monthly deposits the father make---the first 1 month after her 9th birthday and the last on her 17th birthday---in order for her to withdraw $7500 on each of her next four birthdays (18th through the 21st)? evaluate (F/P, 15% 44) Use linear interpolation to determine the value of n corresponding to A/G = 9.0000 if i=7% per year compounded annually. What will be the monthly payment on a 30-year, $550,000 mortgage loan, where the interest rate is 6% per year compounded monthly? What is the annual interest rate corresponds to a nominal interest rate of 12.50% compounded continuously?

Explanation / Answer

1. Let he deposits $ A per months till her 17th birthday Then future value of this annuity = A[{(1+k)^n - 1}/k] = A[(1+0.06/12)^96 -1 ] / (0.06/12) = A (1.005^96 -1 )/0.005 and value of all withdraws at 17th birthday = 7500/(1+0.06) + 7500/ (1+0.06)^2 + 7500/ (1+0.06)^3 + 7500/ (1+0.06)^4 = $ 25988.29 i.e. A (1.005^96 -1 )/0.005 = 25988.29 So A = $211.58 ............... 2. a) F/P = (1+k)^n = (1+0.15)^44 = 468.5 .............. 3. Present Value = 550000 = A[{1-(1/1.005)^360}/0.005] ie A= $ 3297.58 ................ 4. r = [ (1+i/n)^n ] - 1 ie r = [(1+.125/12)^12 ]-1 = 0.1324 = 13.24%

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