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Abram invests N$15500 COMPOUND YEARLY: Rhoda N$17000 COMPOUND QUARTERLY AND RAUNA A SINGLE AMOUNT OF N$ 18 500(INTEREST COMPOUNDED SEMI-ANNUALLY) a) how much will each of them have after 10 years if the interest rate is 15% p.a.? b)determine the interest amount for each of them. c)Which investment is the best?

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sqdancefan

Answer:

  (a), (b) see below

  (c) it depends on the criterion for "best"

Step-by-step explanation:

a) The effective annual rate for 15% compounded n times per year is ...

  (1 +0.15/n)^n

Then the balance after 10 years will be the original balance multiplied by ...

  (1 +0.15/n)^(10n)

For the given accounts, the balances are ...

  • Abram: $62,706.14
  • Rhoda: $74,126.44
  • Rauna: $78,585.25

__

b) The interest earned is the difference between the account balance and the initial investment:

  • Abram: $47,206.14
  • Rhoda: $57,126.44
  • Rauna: $60,085.25

__

c) For a given amount invested, the quarterly compounding will give a higher return than any compounding of less frequency. Over the 10-year period here, investing more money will give a larger amount of earnings, so Rauna's investment is obviously the best.

However, in the long term, the additional compounding wins out, regardless of the amount initially invested. Rhoda's investment, compounded quarterly, will exceed all others after 33 years.