Annual growth factor of a savings account with monthly compounding and the year its value first doubles
Annual growth factor of a savings account with monthly compounding and the year its value first doubles
6 marks
On \(1\) January \(2024\), a sum of \(\$P\) is placed in a savings account. The account pays interest at a nominal annual rate of \(4.2\%\), compounded monthly.
The balances in the account on 31 December of each year form a geometric sequence with common ratio \(r\).
- Find \(r\), correct to \(4\) significant figures.[3]
No money is added to or taken from the account at any time.
- Find the year during which the balance first reaches twice the sum originally placed in the account.[3]
Solution:
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Answer:(a) \(r=1.043\) (b) \(2040\)
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