Question

The future value of an investment of P dollars compounded n times per year with an APR of 100r% (this means r is the decimal) and a length of t years is given by F(P,r,n,t) = P ?1 + r ?nt dollars. Find and write a sentence of interpretation for the following % (this means r is the decimal) and a length of t years is given by F (P, r, n, t) = P (1 + r/n)^nt dollars. Find and write a sentence of interpretation for the following:

(a) Find and write a sentence of interpretation for F ( 32000, 0.54, 12, 4).

(b) Write a complete model for (∂F/∂r)

(C) Write a sentence of interpretation for ∂F/∂t (RIGHT HERE THERE IS A STRAIGHT LINE DOWN WITH THE STUFF TO THE RIGHT AT THE VERY BOTTOM OF THE VERTICAL LINE) (P,r,n,t)=( 32000, 0.54,12, 4).

(The t is not a typo!)

Answer 1

we are given

(A)

we have to find

F ( 32000, 0.54, 12, 4)

we can plug

P=32000 , r=0.54 , n=12, t=4

we can simplify it

..........Answer

Interpretation:

The future value of an investment of 32000 dollars compounded 12 times per year with an APR of 54% and a length of 4 years is 264686.578

(B)

we can find partial derivative with respect to r

now, we can simplify it

...........Answer

(C)

we can find partial derivative with respect to t

.............Answer