Question

1. What is the future value of $100 invested today at 6 percent for four years?
2. What is the present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent?
3. What is the future value of $200 invested today at 8 percent for three years?

Answer 1

Future value of $100 invested today at 6% for 4 years:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $100, r = rate of interest = 6%, n= time period = 4

now, putting theses values in the above equation, we get,

FV = $100 * (1 + 6%)⁴

FV = $100 * (1 + 0.06)⁴

FV = $100 * (1.06)⁴

FV = $100 * 1.26247696

FV = $126.25

So, future value is $126.25

Present value of $100 to be received 10 years from today at 9%:

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value = $100, PV = Present value, r = rate of interest = 9%, n= time period = 10

now, putting theses values in the above equation, we get,

PV = $100 / (1 + 9%)¹⁰

PV = $100 / (1 + 0.09)¹⁰

PV = $100 / (1.09)¹⁰

PV = $100 / 2.367363674

PV = $42.24

So, present value is $42.24

Future value of $200 invested today at 8% for 3 years:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $200, r = rate of interest = 8%, n= time period = 3

now, putting theses values in the above equation, we get,

FV = $200 * (1 + 8%)³

FV = $200 * (1 + 0.08)³

FV = $200 * (1.08)³

FV = $200 * 1.259712

FV = $251.94

So, future value is $251.94