If $800 is invested at interest rate i, compounded annually, in 5 yr it will gro

Question

If $800 is invested at interest rate i, compounded annually, in 5 yr it will grow to an amount A given by A = $800 (1 + i)^5 Find the rate of change, dA/di Interpret the meaning of dA/di. (Simplify your answer. Use integers or fractions for any numbers in the expression. Do not include the $ symbol in your answer.) Choose the correct answer below. dA/di is the rate at which A changes due to changes in the number of years passed. dA/di is the rate at which A changes due to changes in the interest rate i. dA/di is the rate at which A changes due to how often interest is compounded. dA/di is the rate at which A changes due to changes in the initial investment.

Explanation / Answer

Answer :

Given that A = 800 ( 1 + i ) 5

a ) Then differentiate with respect to i on both sides of the above equation

dA/di = 800 [ 5 ( 1 + i ) 4 ]

dA/di = 4000 ( 1 + i ) 4

b ) dA/di is the rate at which A changes due to changes in the interest rate i .

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