What\'s the present value, when interest rates are 8.5 percent, of a $135 paymen

ID: 2654070 • Letter: W

Question

What's the present value, when interest rates are 8.5 percent, of a $135 payment made every year forever?

What's the present value of a $910 annuity payment over four years if interest rates are 8 percent?

Compute the present value of a $3,800 deposit in year 1 and another $3,300 deposit at the end of year 3 if interest rates are 10 percent.

What is the future value of a $920 annuity payment over six years if interest rates are 10 percent?

Compute the future value in year 8 of a $2,300 deposit in year 1 and another $1,800 deposit at the end of year 3 using a 10 percent interest rate

How long will it take $2,000 to reach $4,400 when it grows at 11 percent per year?

What's the present value of a $910 annuity payment over four years if interest rates are 8 percent?

Compute the present value of a $3,800 deposit in year 1 and another $3,300 deposit at the end of year 3 if interest rates are 10 percent.

What is the future value of a $920 annuity payment over six years if interest rates are 10 percent?

Compute the future value in year 8 of a $2,300 deposit in year 1 and another $1,800 deposit at the end of year 3 using a 10 percent interest rate

How long will it take $2,000 to reach $4,400 when it grows at 11 percent per year?

(1) A forever payment is called a perpetuity.

Present value of a perpetuity = Annual fixed payment /Interest rate

= $ 135 / 0.085 = $1,588.24

(2) Total Present Value (PV) = PV of $3,800 after year 1 + PV of $3,300 after year 3 [Both discounted at 10%]

= [$3,800 / 1.1] + [$3,300 / (1.1)3]

= $[3,454.55 + 2,479.34]

= $5,933.89

(3) Future Value of $920 annual annuity

= $920 x Future Value Interest Factor of Annuity at 10%, 6 years

= $920 x 7.7156 (From FVIFA table)

= $7,098.35

(4) Total Future Value at end of Year 8 = FV of $2,300 in Year 1 (7 years left) + FV of $1,800 in Year 3 (5 years left)

= [$2,300 x Future Value Interest Factor (7 years, 10%)] + [$1,800 x Future Value Interest Factor (5 years, 10%)]

= [$2,300 x 1.9487] + [$1,800 x 1.6105] (Using FVIF table)

= $[4,482.01 + 2,898.9] = $7,380.91

(5) Future Value = Present Value x (1 + Interest rate) Number of Years

4,400 = 2,000 x (1.11)N

Or, (1.11)N = 4,400 / 2,000 = 2.20

Taking logarithms on both sides:

N Log 1.1 = Log 2.2

Or, N = Log 2.2 / Log 1.1 = 0.7885 / 0.0953 = 8.27 years

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.