Answer :
To find the discounted value given an 8% growth rate per year over 10 years, we will use the formula for the present value. Therefore, the discounted value of $197 using an 8% growth per year for 10 years is approximately $91.24.
To find the discounted value given an 8% growth rate per year over 10 years, we will use the formula for the present value. This formula is based on the future value of money being discounted to the present day, which in finance is often called "discounting."
The formula for the present value (PV) of money, given a future value (FV), an annual growth rate (r), and a number of years (t) is:
[tex]\[ PV = \frac{FV}{(1 + r)^t} \][/tex]
In this case, the future value (FV) is $197, the annual growth rate (r) is 8% (or 0.08 as a decimal), and the time (t) is 10 years. Plugging these values into the formula gives us:
[tex]\[ PV = \frac{197}{(1 + 0.08)^{10}} \][/tex]
First callculate (1 + 0.08)¹⁰ which means we need to multiply 1.08 by itself 10 times:
(1 + 0.08)¹⁰ ≈ 2.158925 (rounded to six decimal places for illustration purposes)
Now we need to divide the future value by this amount:
[tex]\[ PV \approx \frac{197}{2.158925} \approx 91.245 \][/tex] (again rounded to three decimal places)
Therefore, the discounted value of $197 using an 8% growth per year for 10 years is approximately $91.24.
