If exist2000 is invested at 4% interest, find the value of the investment at the

Question

If exist2000 is invested at 4% interest, find the value of the investment at the end of 7 years if the interest is compounded as follows. (Round your answers to the nearest cent) (i) annually exist (ii) semiannually exist (III) monthly exist (iv) weekly exist (v) daily exist (vi) continuously exist (b) If A(t) is the amount of the investment at time t for the case of continuous compounding, write a differential equation satisfied by A(t). dA/dt = Find the initial condition satisfied by A(t). A(0) =

Explanation / Answer

We have to use the following formula

A=P(1+(r/n))nt

i ) annually

A=2000(1+.04)7 =2000(1.04)7 =$2631.9

ii) semiannually

A=2000(1+(.04÷2))2*7 =2000(1.02)14 =$2639

iii) monthly

A=2000(1+(.04/12))12*7=2645

iv) weekly

A=2000(1+(.04/52))52×7 = 2646

v) A=2000(1+(.04/365))365*7=2646.2

vi)

continuously

A=pert

A=2000e.04*7=2646.3

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