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(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?

(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?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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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