Question 1088346
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We have two investment plans 


Investment Plan A: The money is compounded monthly with annual interest rate of 5.4%
Investment Plan B: The money is compounded quarterly with annual interest rate of 5.5%


For both plans A and B, the same amount of money ($11,000) is deposited for the same time duration (5 years).


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For both plans, we'll use the compound interest formula
A = P(1+r/n)^(n*t)


where,
A = amount in the account after t years
P = initial amount invested
r = interest rate (in decimal form)
n = compounding frequency
t = number of years


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Investment Plan A:


We invest $11,000 over 5 years at 5.4% compounded monthly


So this means,
P = 11000
r = 0.054 (since 5.4% = 5.4/100 = 0.054)
n = 12 (monthly ---> compounding 12 times a year)
t = 5


Plug all those values into the formula to get
{{{A = P(1+r/n)^(n*t)}}}
{{{A = 11000(1+0.054/12)^(12*5)}}}
{{{A = 11000(1+0.0045)^(12*5)}}}
{{{A = 11000(1.0045)^(12*5)}}}
{{{A = 11000(1.0045)^(60)}}}
{{{A = 11000(1.30917126694449)}}}
{{{A = 14400.8839363894}}}
{{{A = 14400.88}}}


Therefore, you'll have $14,400.88 in the account if you go with investment plan A. 


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Investment Plan B:


We invest $11,000 over 5 years at 5.5% compounded quarterly


The values are,
P = 11000
r = 0.055 (since 5.5% = 5.5/100 = 0.055)
n = 4 (quarterly ---> compounding 4 times a year)
t = 5


Plug all those values into the formula to get
{{{A = P(1+r/n)^(n*t)}}}
{{{A = 11000(1+0.055/4)^(4*5)}}}
{{{A = 11000(1+0.01375)^(4*5)}}}
{{{A = 11000(1.01375)^(4*5)}}}
{{{A = 11000(1.01375)^(20)}}}
{{{A = 11000(1.31406650176068)}}}
{{{A = 14454.7315193675}}}
{{{A = 14454.73}}}


Therefore, you'll have $14,454.73 in the account if you go with investment plan B.

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In summary, you'll have...

<ul>
<li>$14,400.88 in the account if you go with investment plan A.</li>
<li>$14,454.73 in the account if you go with investment plan B.</li>
</ul>

We see that investment plan B is the winner with the larger amount of money. 

 
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