Question

1. What is the Present Value of an ORDINARY ANNUITY that has 12 annual payments of 3000 if the return is 12 % 2. What is the Present Value of a monthly annuity that pays $ 250 per year for 10 years when investments make 9 % return annually. 3. Find the future value of 250,000 invested for 10 years at 12%. 4. Find the Future value of an annuity due of 450 per month for 3 years when returns are 10 % annually,

Answer 1

1. N = 12

PMT = 3000

r = 12%

The present value of an ordinary annuity:

$PV = \frac{PMT}{ r } * \left [ 1 - \frac{1}{(1+ r )^{ n }} \right ]$

$PV = \frac{3,000}{ 0.12 } * \left [ 1 - \frac{1}{(1+ 0.12 )^{ 12 }} \right ]$

PV = 25,000 * 0.7433249071

PV = $18,583.1226775

2. The payments are monthly in a monthly annuity

n = 10 * 12 = 120 payments

PMT = 250

r = 9%/12 = 0.0075

$PV = \frac{PMT}{ r } * \left [ 1 - \frac{1}{(1+ r )^{ n }} \right ]$

250 PV = 0,0075 * 1 (1+0.0075) 120

PV = 33, 333.3333333333 * 0.592062695

PV = $19,735.4231666666

3. FV = PV * (1 + r)^n

FV = 250,000 * (1 + 0.12)^10

FV = $776,462.052086052

4. Future value of annuity due

n = 3 * 12 = 36

r = 10%/12 = 0.008333333333

PMT = 450

PMT FV = -*[(1 + r)" – 1] *(1+r)

450 FV = იცივვვვვვვვვ — * [(1 + 0.008333333333)36 – 17 (1+0.008333333333)

FV = 54.000.00000216 * 0.3481818424*(1 +0.008333333333)

FV = $18,958.5013194321

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