(a) What is the present of an ordinary annuity of $325 per month  for 4 years at 6% interest compounded monthly? (b) What is the present value of this investment if it is an annuity due?

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Problem #2. Take a look at example 6 from section 12-6 named "Calculating Present Value of an Annuity by Formula". Solve the following problem using formulas only. Show your work.

(a) What is the present of an ordinary annuity of $325 per month  for 4 years at 6% interest compounded monthly?

(b) What is the present value of this investment if it is an annuity due?

Example 6
Calculating Present Value of an Annuity by Formula
a. What is the present value of an ordinary annuity of $100 per month for 4 years at 6% interest
compounded monthly?
b. What is the present value of this investment if it is an annuity due?
Solution Strategy
a. For this present value of an ordinary annuity problem, we use i = .5% (6% ÷ 12) and
n = 48 periods (4 years x 12 periods per year).
1- (1+i)"
PV = Pmt x
-48
(1+.005)
PV = 100 x
.005
-48
1- (1.005)
PV = 100 X
.005
1-.7870984111
PV = 100 x
.005
.2129015889
PV= 100 ×
.005
PV = 100 × 42.58031778 = $4,258.03
Calculator Sequence:
1 + .005
yx 48 +/- M+ 1
MR = +.005 x 100
$4,258.03
b. To solve as an annuity due rather than an ordinary annuity, multiply the present value of the
ordinary annuity by (1 + i) for one extra compounding period.
(1+ i) × PVordinary annuity
(1+ .005) x 4,258.03
PVannuity due
PVannuity due
PVannuity due = (1.005) × 4,258.03 = $4,279.32
Calculator Sequence: 1 + .005
x 4,258.03
$4,279.32
Transcribed Image Text:Example 6 Calculating Present Value of an Annuity by Formula a. What is the present value of an ordinary annuity of $100 per month for 4 years at 6% interest compounded monthly? b. What is the present value of this investment if it is an annuity due? Solution Strategy a. For this present value of an ordinary annuity problem, we use i = .5% (6% ÷ 12) and n = 48 periods (4 years x 12 periods per year). 1- (1+i)" PV = Pmt x -48 (1+.005) PV = 100 x .005 -48 1- (1.005) PV = 100 X .005 1-.7870984111 PV = 100 x .005 .2129015889 PV= 100 × .005 PV = 100 × 42.58031778 = $4,258.03 Calculator Sequence: 1 + .005 yx 48 +/- M+ 1 MR = +.005 x 100 $4,258.03 b. To solve as an annuity due rather than an ordinary annuity, multiply the present value of the ordinary annuity by (1 + i) for one extra compounding period. (1+ i) × PVordinary annuity (1+ .005) x 4,258.03 PVannuity due PVannuity due PVannuity due = (1.005) × 4,258.03 = $4,279.32 Calculator Sequence: 1 + .005 x 4,258.03 $4,279.32
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