Pregunta
Convert an interest rate of
p.a. compounded quarterly to an annual effecti
interest rate.
A lawnmower was traded in for R 236 after 10 years. The depreciation was
calculated at
p.a. on a straight-line basis.
Determine the cost of the lawnmower 10 years ago.
interest rate.
A lawnmower was traded in for R 236 after 10 years. The depreciation was
calculated at
Determine the cost of the lawnmower 10 years ago.
Ask by Cummings Wilson. in South Africa
Jan 07,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
1. Interest Rate Conversion:
- Nominal Annual Rate: 10% per annum, compounded quarterly.
- Annual Effective Interest Rate: Approximately 10.38%.
2. Lawnmower Cost:
- Depreciated Value after 10 Years: R236.
- Depreciation Rate: 9.2% per annum.
- Original Cost 10 Years Ago: R2,950.
Solución

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Beyond the Answer
To convert the interest rate of
p.a. compounded quarterly to an effective annual interest rate, you can use the formula:
where
is the nominal interest rate,
is the number of compounding periods per year, and
is the number of years. Substituting the values, we have:
So, the effective annual interest rate is approximately
.
To determine the cost of the lawnmower 10 years ago, we can apply the straight-line depreciation formula:
Here, the current value after 10 years is R 236, and the depreciation rate is
per annum. The total depreciation over 10 years is:
Therefore,
, which simplifies to
. Thus, the cost of the lawnmower 10 years ago is:

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