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How much will $1000 be worth in three years if it earns 4% interest, compounded monthly? Compare that to the amount earned when interest is compounded yearly. Which is the better investment and why?

a) $1124 compounded monthly; $1120 compounded yearly
b) $1120 compounded monthly; $1124 compounded yearly
c) $1160 compounded monthly; $1120 compounded yearly
d) $1120 compounded monthly; $1160 compounded yearly

User Ghazni
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1 Answer

5 votes

Final answer:

The future value of a $1000 investment with 4% interest compounded monthly will be $1123.60, while with yearly compounding it will be $1124.86. Therefore, the better investment option is to compound the interest yearly for a higher future value.

So, the correct answer is B.

Step-by-step explanation:

To calculate the future value of an investment with compound interest, we can use the formula:

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

Where:

  • A is the future value of the investment
  • P is the principal amount (the initial investment)
  • r is the annual interest rate (written as a decimal)
  • n is the number of times interest is compounded per year
  • t is the number of years

In this case, we have:

  • P = $1000
  • r = 4% = 0.04
  • n = 12 (compounded monthly)
  • t = 3

Using this information, we can calculate the future value of the investment with monthly compound interest:

A = 1000(1+0.04/12)^(12*3) = $1123.60

Next, we can calculate the future value of the investment with yearly compound interest:

A = 1000(1+0.04)^3 = $1124.86

Comparing these values, we can see that the investment with monthly compound interest ($1123.60) is lower than the investment with yearly compound interest ($1124.86).

Therefore, the better investment option is to compound the interest yearly because it results in a higher future value ($1124.86).

So, the correct answer is B.

User Naili
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