Determine the current amount of money that must be invested at 6% nominal interest, compounded monthly, to provide an

Question

Determine the current amount of money that must be invested at 6% nominal interest, compounded monthly, to provide an annuity of $15,000 (per year) for 5 years, starting 9 years from now. The interest rate remains constant over the entire period of time.

Help In Homework · Accepted Answer

Step 1 Caluculation of Effective rate of Interest EAR = [ ( 1 + r ) ^ n ] - 1 = [ ( 1 + 0.005 ) ^ 12 ] - 1 = [ ( 1.005 ) ^ 12 ] - 1 = [ 1.0617 ] - 1 = 0.0617 I.e EAR is 6.17 % Step 2: Calculation of FV of Annutiy PV of Annuity Particulars Amount Cash Flow $ 15,000.00 Int Rate 6.1700% Periods 5 PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r = $ 15000 * [ 1 - [(1+0.0617)^-5]] /0.0617 = $ 15000 * [ 1 - [(1.0617)^-5]] /0.0617 = $ 15000 * [ 1 - [0.7413]] /0.0617 = $ 15000 * [0.2587]] /0.0617 = $ 62894.31 Step 3: Caluculation annutity Value today Particulars Amount Future Value $ 62,894.00 Int Rate 6.170% Periods 8 Present Value = Future Value / ( 1 + r )^n = $ 62894 / ( 1 + 0.0617 ) ^ 8 = $ 62894 / ( 1.0617 ) ^ 8 = $ 62894 / 1.6144 = $ 38957.82 Present Value: PV = FV / (1+r)^n Where r is Int rate per period n - No. of periods

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Determine the current amount of money that must be invested at 6% nominal interest, compounded monthly, to provide an annuity of $15,000 (per year) for 5 years, starting 9 years from now

Expert Solution

Archived Solution

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.005 ) ^ 12 ] - 1
= [ ( 1.005 ) ^ 12 ] - 1
= [ 1.0617 ] - 1
= 0.0617
I.e EAR is 6.17 %

PV of Annuity
Particulars	Amount
Cash Flow	$ 15,000.00
Int Rate	6.1700%
Periods	5

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 15000 * [ 1 - [(1+0.0617)^-5]] /0.0617
= $ 15000 * [ 1 - [(1.0617)^-5]] /0.0617
= $ 15000 * [ 1 - [0.7413]] /0.0617
= $ 15000 * [0.2587]] /0.0617
= $ 62894.31

Particulars	Amount
Future Value	$ 62,894.00
Int Rate	6.170%
Periods	8

Present Value = Future Value / ( 1 + r )^n
= $ 62894 / ( 1 + 0.0617 ) ^ 8
= $ 62894 / ( 1.0617 ) ^ 8
= $ 62894 / 1.6144
= $ 38957.82