Question

Time value—Annuities Marian Kirk wishes to select the better of two 5-year annuities, C and D. Annuity Cis an ordinary annuity of $2,500 per year for 5 years. Annuity D Is an annuity due of $2,200 per year for 5 years.
a. Find the future value of both annuities at the end of year 5, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.
b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 5 for both the (1) 10% and (2) 20% Interest rates.
c. shows the future value of ordinary and due through time line on the above solutions.

Answer 1

(a) Future value of

(1) ordinary annuity (C) at 10%

$P=PMT×[((1+r)^n-1)/r]$

where,

P= future value

PMT=Amount of each annuity

r=interest value

n=period

$P=2500×[((1+0.1)^5-1)/0.1]$

$P=2500×[(1.1^5-1)/0.1]$

$P=2500×6.1051$

P=$15262.75

annuity due (D) at 10%.

$P={PMT×[((1+r)^n-1)/r]}×(1+r)$

where,

P= future value

PMT=Amount of each annuity

r=interest value

n=period

$P={2200×[((1+0.1)^5-1)/0.1]}×(1+0.1)$

$P={2200×[(1.1^5-1)/0.1]}×(1.1)$

P=$14774.34

(2)Future value of

ordinary annuity (C) at 20%.

$P=2500×[((1+0.2)^5)-1)/0.2]$

$P=2500×7.4416$

P=$18604

annuity due (D) at 20%.

$P={2200×[((1+0.2)^5)-1)/0.2]}×(1+0.2)$

$P=2200×[(1.2^5-1)/0.2]×(1.2)$

$P=2200×7.4416×(1.2)$

P=$19645.82

(b) Annuity with best future value.

(1) at 10% - annuity C with value of $15262.75

(2) at 20% - annuity D with value of $19645.82

(c)Future value using timeline.

(1) at 10%

(2)at 20%