Question

2)What is the relationship between the present-value factor and the annuity present-value factor?

3)What will $5,000 invested for 10 years at 8 percent compounded annually grow to? How many years will it take $400 to grow to $1,671 if it is invested at 10 percent compounded annually? At what rate would $1,000 have to be invested to grow to $4,046 in 10 years?

7)What is the future value of an ordinary annuity of $1,000 per year for 7 years compounded at 10%? What would be the future value if it were an annuity due?

Answer 1

2) Relationship between the present-value factor and the annuity present-value factor

We have

present-value factor (PVF) = (1+r)^-n and

annuity present-value factor = (1-(1+r)^-n)/r

annuity present-value factor = (1-PVF)/r

3)What will $5,000 invested for 10 years at 8 percent compounded annually grow to?

Future Value = Present Value * (1+r)^n

= 5000 * (1.08)^10

= 5000*2.15892499727

= 10794.62

-How many years will it take $400 to grow to $1,671 if it is invested at 10 percent compounded annually?

Let n be the no. of years

Future Value = Present Value * (1+r)^n

1671 = 400 * (1.1)^n

(1.1)^n = 1671/400 = 4.1775

n = log4.1775 / log1.1

= 0.62091645856/0.04139268515

n = 15 years

-At what rate would $1,000 have to be invested to grow to $4,046 in 10 years?

Future Value = Present Value * (1+r)^n

4046 = 1000 * (1+r)^10

(1+r)^10 = 4046/1000 = 4.046

1+r = 4.046^(1/10) = 1.15001257129

r = 1.15001257129-1

=.15001257129

r = 15%

7)What is the future value of an ordinary annuity of $1,000 per year for 7 years compounded at 10%?

Future value of Annuity = A [((1+r)ⁿ-1) / r]

Where

A - Annuity payment = 1000

r - rate per period = 10%

n - no. of periods = 7

Future value of Annuity = 1000 [((1.1)^7 -1) / .1]

= 1000*9.487171

= 9487.17

Future value of Annuity Due = A [((1+r)ⁿ-1) / r] * (1+r)

= 1000 [((1.1)^7 -1) / .1] * 1.1

= 1000 * 10.4358881

= 10,435.89