(a) If $3000 is invested at 6% interest, find the value of the investment at the
ID: 2885953 • Letter: #
Question
(a) If $3000 is invested at 6% interest, find the value of the investment at the end of four years if the interest is compounded as follows. (Round your answers to two decimal places.) (i) annually $ Incorrect: Your answer is incorrect. (ii) quarterly $ Incorrect: Your answer is incorrect. (iii) monthly $ Incorrect: Your answer is incorrect. (iv) weekly $ (v) daily $ (vi) continuously $ (b) If the interest is compounded quarterly, how long will it take for the balance to double? (Round your answer to two decimal places.) years (c) How long will it take for the value of the investment to double if interest is compounded continuously? (Round your answer to two decimal places.) years
Explanation / Answer
A= P(1+(r/n))nt
a. i . A=3000(1+0.06)4=3000(1.06)4=$3787.43
ii. A = 3000(1+0.06/4)4*4 = 3000(4.06/4)16=$3806.96
iii. A= 3000(1+0.06/12)12*4=3000(12.06/12)48 = $3811.47
iv. A= 3000(1+0.06/52)52*4=$3813.22
v. A= 3000(1+0.06/365)365*4 =$3813.67
vi . A= p ert =3000 e0.06*4 =$3813.74
b. 2P=P(1+0.06/4)4t
log 2= 4t(log(4.06/4)
t=11.64
c.2P=P e0.06t
ln 2 =0.06t
t=11.55
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