SOLUTION: Use the compound interest formulas A=P (1 + r/n)^nt and A=pe^rt Suppose that you have $11,000 to invest. Which investment yields the greater return over 5 years: 5.4% compounded

Algebra ->  Finance -> SOLUTION: Use the compound interest formulas A=P (1 + r/n)^nt and A=pe^rt Suppose that you have $11,000 to invest. Which investment yields the greater return over 5 years: 5.4% compounded      Log On


   

Question 1088346: Use the compound interest formulas A=P (1 + r/n)^nt and A=pe^rt
Suppose that you have $11,000 to invest. Which investment yields the greater return over 5 years: 5.4% compounded monthly or 5.5% compounded quarterly?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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%281%2Br%2Fn%29%5E%28n%2At%29
A+=+11000%281%2B0.054%2F12%29%5E%2812%2A5%29
A+=+11000%281%2B0.0045%29%5E%2812%2A5%29
A+=+11000%281.0045%29%5E%2812%2A5%29
A+=+11000%281.0045%29%5E%2860%29
A+=+11000%281.30917126694449%29
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%281%2Br%2Fn%29%5E%28n%2At%29
A+=+11000%281%2B0.055%2F4%29%5E%284%2A5%29
A+=+11000%281%2B0.01375%29%5E%284%2A5%29
A+=+11000%281.01375%29%5E%284%2A5%29
A+=+11000%281.01375%29%5E%2820%29
A+=+11000%281.31406650176068%29
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...

  • $14,400.88 in the account if you go with investment plan A.

  • $14,454.73 in the account if you go with investment plan B.


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