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1 vote
If $10000 is invested in an account with a 3% nominal interest rate, compounded monthly. (a) Find the exact amount in the account after 5 years and after 10 years. (b) Find the approximate amount (rounded to the nearest penny) in the account after 5 years and after 10 years. (c) Write, but do not solve an equation that would determine how long it would take for the account to be worth $20000. (d) Write, but do not solve an equation that would determine how long it would take for the account to be worth $40000.

asked
User Rez
by
7.3k points

1 Answer

3 votes
  • Answer: 40000 = 10000( 1 + 0.03/12)^12t

(a) - The Exact Amount in the Account After Five (5) Years is

10000(1 + 0.03/12)^12 * 5 and After Ten (10) Years is 10000(1 + 0.03/12)^12 * 10

(b) - The Approximate Amount in the Account After Five (5) Years is $11618.37 and After Ten (10) Years is $1348.29

(c) - The Equation to determine how long it would take for the account to be worth $20000 is: 20000 = 10000(1 + 0.03/12)^12t

(d) - The Equation to Determine How long it would take for the Account to be worth $40000 is 40000 = 10000( 1 + 0.03/12)^12t

  • Explanation:

MAKE A PLAN:

Use the FORMULA for COMPOUND INTEREST:

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

  • Where "A" is:

Where, A = FINAL AMOUNT

Where, P = PRINCIPAL

Where, r = NOMINAL INTEREST RATE

Where, n = NUMBER of TIMES INTEREST COMPOUNDED PER YEAR

Where, t = NUMBER of YEARS

  • SOLVE THE PROBLEM:

(a) - EXACT AMOUNT after FIVE (5) Years, and TEN (10) YEARS:

  • (1) - AFTER FIVE (5) YEARS:

A = 10000(1 + 0.03/12)^12 * 5

  • (2) - AFTER TEN (10) YEARS:

A = 10000(1 + 0.03/12)^12 * 10

  • (b) - APPROXIMATE AMOUNT AFTER FIVE (5) YEARS, and TEN (10) YEARS:
  • (1) - After Five (5) Years: ≈

A ≈ 11618.37

  • (2) - After Ten (10) Years:

A ≈ 13486.29

  • (c) - Equation for the Account to be worth 20000:

20000 = 10000(1 + 0.03/12)^12t

  • (d) - Equation for the Account to be worth 40000:

40000 = 10000(1 + 0.03)^12t

  • Draw the conclusion:

(d) - The Equation to Determine How long it would take for the Account to be worth $40000 is 40000 = 10000( 1 + 0.03/12)^12t

I hope this helps you!

answered
User Gbinflames
by
8.9k points
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