Question

please show all steps, I need help on part D. Thanks!

row detailed and appropriate cash flow diagrams for each problem, and use quations to solve each problem. Show and explain all work Facter Name ormula Converts to given P to P given F to A given F to A given fP to F given A to P given A Single Payment Compound Amount (F/P, ma, n) P/F, P%, n) AF.%, n) (AP, ins, n) Single Payment Present Worth Uniform Series Sinking Fund I+ ir Capital Recovery Uniform Series Compound Amount (FIA, %,) (P/A, i%, n) Uniform Series Present Worth Solve the following problems with the rate of interest equal to 9% compounded annually: (a) If $20,000 is invested today, what will be its value after 5 years? 10 years? (b) How long will it take for invested money to double in value? (c) If S1,500 is invested today, and an equal amount is invested each year for 6 years (seve 1-1 payments), what will be the value after the last payment in 6 years? After 10 years? (d) if $140,000 is needed at the close of 5 years, what equal annual payment must be made starting today and ending at the close of 4 years (ive payments)?

Answer 1

1-1)
d)	The 5 annual payments to be made constitute an annuity due as
	the payments are to be made at the beginning of the year.
	The $140000 needed at EOY 5 is the future value of this annuity
	due.
	The formula for finding future value of annuity due = FVA = A*(1+r)*((1+r)^n-1))/r
	Where
	A = The annual payment made the beginning of each year
	r = the interest rate
	n = number of years
	The above formula can be used to find out A, guven FVA
	A = FVA*r/[(1+r)*((1+r)^n-1))]
	Substituting values we have, A = 140000*0.09/((1.09)*(1.09^5-1)) =	$ 21,461.42
	Answer: $21,461.42
	NOTE:
	The formulae given are for ordinary annuities not for annuities due.
	Hence, the formula has been derived.