Question

1. Assume you will invest $850 this year, $1,200 one year from now, $1,250 two years from now, $1,550 three years from now, $1,540 four years from now, and $1,250 five years from now. Assuming the interest rate of 11.9% and that it will compound annually, what will be the future value of these investments five years from now?

2. Assume ABC Corp. will earn $450 this year, $600 one year from now, $600 two years from now, $800 three years from now, $950 four years from now, and $1,200 five years from now. Assuming the interest rate of 12.8% and that it will compound annually, what will be the total present value of ABC Corp.’s earnings?

~These questions are completely unrelated to each other

Answer 1

1. For calculating future value of any amount we need to multiply interest rate with the amount

for 1st year FV = amount * interest

for 2nd year FV = (amount * interest) * interest because interest is compunded annually and so on for next year

LEts calculate Future value of given investment

assume investment is made at te beginning of each year

denote Investment with I

I₀= $ 850, I₁=$ 1200, I₂= $ 1250, I₃= $ 1550, I₄= $ 1540, I₅= $ 1250

FV = 850* (1.119)⁵ + 1200* (1.119)⁴ + 1250* (1.119)³ + 1550* (1.119)⁴ + 1540* (1.119)⁵ + 1250

FV = 1491.315 + 1881.4886 + 1751.46 + 1940.85 + 1622.55 + 1250

FUTUE VAUE OF THESE INVEST MENT = $ 9937.664

2. For calculating present value value of any amount we need to divide interest rate with the amount

for 1st year PV = amount / interest

for 2nd year PV = (amount / interest) / interest because interest is compunded annually and so on for next year

LEts calculate Present value of given earning

assume earning is earn at beginning of each year

denote earning with E

E₀= $ 450, E₁=$ 600, E₂= $ 600, E₃= $ 800, E₄= $ 950, E₅= $ 1200

PV = 450 + 600 / (1.128) + 600 / (1.128)² + 800 / (1.128)³ + 950 / (1.128)⁴ + 1200 / (1.128)⁵

PV = 450 + 531.91 + 471.56 + 557.4 + 586.79 + 657.11

PRESENT VALUE OF THESE EARNINGS = $ 3254.77

THE AMOUNT 450 IS NOT DIVIDE WITH INTEREST BECAUSE WE CALCULATE PV AT 0th TIME AND 450 WAS EARN AT 0th TIME