a=16,00, r=11.5%, t=5 years
determine the present value, p, you must invest to have the future value, a, at simple interest rate r after time t. round uo to nearest cent
I assume
a=$16,000, and
r=11.5% compounded yearly.
So
a=p(1+r)^n
=p(1.115)^5
p=16000/(1.115^5)
=$9284.22
A = $9053.50, r = 13.5%, t = 17 months
To determine the present value, P, you must invest to have the future value, A, at a simple interest rate, r, after time, t, you can use the formula for simple interest:
A = P + P * r * t
Rearranging the formula, we get:
P = A / (1 + r * t)
Now, let's plug in the given values:
A = $16,000 (future value)
r = 11.5% (interest rate expressed as a decimal, so r = 0.115)
t = 5 years
P = 16,000 / (1 + 0.115 * 5)
P = 16000 / (1 + 0.575)
P = 16000 / 1.575
P ≈ $10,159.49 (rounded to the nearest cent)
Therefore, you must invest approximately $10,159.49 to have a future value of $16,000 at a simple interest rate of 11.5% after 5 years.