Question

In this problem you will compare the effects of different compounding periods on the interest an investment earns. Complete the table below using the values indicated. Show the formula you used, with the correct values, in the second column. In the third column, give the result, rounded to the nearest cent.
Principal: $1,000
APR: 4.5%
Time: 10 years

Find the equations for annually, quarterly, monthly and daily

Answer 1

Answer:

  see attached

Step-by-step explanation:

You are asked to use the compound interest formula for different values of n, the number of times per year the interest is compounded.

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The basic formula is ...

  A = P(1 +r/n)^(nt)

for the amount in an account in which principal P earns interest at annual rate r compounded n times per year for t years.

The problem statement gives values for P, r, t, so we only need to compute the result for different values of n. With the given values filled in, the formula is ...

  A = 1000(1 +0.045/n)^(10n)

Values of n to be used are ...

• annually: n = 1
• quarterly: n = 4
• monthly: n = 12
• daily: n = 365

The formula you will evaluate uses these values where 'n' is in the formula. Corresponding account balances are ...

• annual compounding: $1552.97
• quarterly compounding: $1564.38
• monthly compounding: $1566.99
• daily compounding: 1568.27

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For repetitive evaluation of the same formula, we like a calculator or spreadsheet. Many calculators have the "time value of money" formulas pre-programmed. This is shown in the second attachment, where the value that varies is "C/Y", the number of compoundings per year.