Answer:
Annual: $302 737.50
Continuous: $332 507.52
Step-by-step explanation:
A. Compounded annually
The formula for <em>compound interest</em> is
A = P(1 + r)ⁿ
Data:
P = $45 000
r = 10 %
t = 20 yr
Calculations:
n = 20
A = 45 000(1+ 0.10)²⁰
= 45 000 × 1.10²⁰
= 45 000 × 6.727 499 95
= $302 737.50
B. Compounded continuously
The formula for <em>continuously compounded inerest</em> is
= 45 000 × 7.389 056 61
= $332 507.52
Given the expression,
We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.
If we have , we will get
by multiplying them. And
.
So here in the problem, we will get,
Now in the numerator we have . We can check 8x is common there. we will take out -8x from it, we will get,
And in the denominator we have . We can check 2 is common there. If we take out 2 from it we will get,
So we can write the expression as
is common to the numerator and denominator both, if we cancel it we will get,
We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,
So we have got the required answer here.
The correct option is the last one.