Repeated changes, weighted percentages and reverse compound growth
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Practise the method.
Repeated changes, weighted percentages and reverse compound growth
Optional enrichment: Repeated changes, weighted percentages and reverse compound growth
Example 1
An account starts with $1600 and earns the same positive annual interest rate for two years. Immediately after the first year's interest is paid, $300 is deposited. After the second year's interest, the balance is $2304.36. Find the annual percentage rate.
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Answer: 11
For multiplier m,(1600m+300)m=2304.36.
The positive multiplier is 1.11
the rate is 11%.
Example 2
A value starts at 1500. It increases by r%, then by 2r%, becoming 2135.7. Find r, given r>0.
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Answer: 13
(1+100r)(1+1002r)=1.4238.
Expand, solve the quadratic and choose the positive root, 13.
Example 3
An account starts with $4300 and earns the same positive annual interest rate for two years. Immediately after the first year's interest is paid, $300 is deposited. After the second year's interest, the balance is $6237.27. Find the annual percentage rate.
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Answer: 17
For multiplier m,(4300m+300)m=6237.27.
The positive multiplier is 1.17
the rate is 17%.
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