Recovering the rate and principal from two balances
Recovering the rate and principal from two balances
IP 2
7 marks
A sum of money is invested at \(r\%\) per annum compounded yearly, with no further deposits or withdrawals. The balance is \(\$5832\) after \(2\) years and \(\$6298.56\) after \(3\) years.
- Find \(r\) and the amount originally invested.[3]
- Show that the interest earned in any year is \(\left(1+\dfrac{r}{100}\right)\) times the interest earned in the year before.[2]
- Find the simple interest rate per annum that would give the same balance after \(3\) years.[2]
Solution:
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Answer:(a) \(r=8\), \(\$5000\) (b) Interest in year \(n\) is \(Pk^{n-1}(k-1)\), so consecutive ratios equal \(k\) (c) \(8.66\%\) (3 s.f.)
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