Question

PLEASE HELP 20 POINTS AND WILL MARK BRAINLIEST YOU NEED TO EXPLAIN Chan deposited money into his retirement account that is compounded annually at an interest rate of 7%. Chan thought the equivalent quarterly interest rate would be 2%. Is Chan correct? If he is, explain why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your answer. (8 pts)

Answer 1

Answer:

He is not correct because it would be less than 2

Step-by-step explanation:

The actual quarterly interest rate would be 0.175.I got this by dividing 0.7 by 4 and you get 0.175. 0.175 is close but it is not 2 which makes Chans statement wrong.

Answer 2

Answer:

Chan is wrong and the equivalent rate of interest is 6.8%.

Step-by-step explanation:

Compound interest for principal P, for r% interest and for t years compounded annually is:

$CI_{1} =P(1+\frac{r}{100})^{t}-P$

For r = 7,

$CI_{1} =P(1+\frac{7}{100})^{t}-P$

$CI_{1} =P(1.07)^{t}-P$ --- (1)

Compound interest for principal P, for r% interest and for t years compounded quarterly is:

$CI_{2} =P(1+\frac{r}{400})^{4t}-P$

For r = 2,

$CI_{2} =P(1+\frac{2}{400})^{4t}-P$

$CI_{2} =P(1.005)^{4t}-P$)

$CI_{2} =P(1.2155)^{t}-P$ --- (2)

Clearly, (1) and (2) are not equal and hence Chan is wrong.

Let r be the equivalent quarterly interest rate.

Then,

$CI=P(1+\frac{r}{400} )^{4t}-P$

$=P(1+0.0025r)^{4t}-P$

Therefore,

$=P(1+0.0025r)^{4t}-P=P(1.07)^{t}-P$

$=P(1+0.0025r)^{4t}=P(1.07)^{t}$

$\frac{(1+0.0025r)^{4t} }{1.07^{t} } =1$

$\frac{(1+0.0025r)^{4} }{1.07} =1$

$(1+00025r)^{4}=1.07$

$1+0.0025r=1.07^{1/4}$

=1.017

0.0025r = 1.017 - 1 = 0.017

$r=\frac{0.017}{0.0025}$

= 6.8%

Hence, the equivalent quarterly interest rate is 6.8%.