MHB Compound Interest Problem: When Will Mr. Weasley's Liabilities Be Cancelled?

AI Thread Summary
The discussion revolves around calculating when a payment of 300,000 galleons will settle Mr. Weasley's liabilities of 100,000 galleons due in 2 years and 150,000 galleons due in 5 years, considering a 12% effective interest rate. Participants emphasize the need to determine the present value (PV) of each liability and the payment, using logarithmic calculations to solve for the time required to cancel the debts. The hint provided suggests using the formula for present value and logarithms to find the solution. Understanding the effective interest rate's impact on future liabilities is crucial for accurate calculations. The thread seeks assistance in resolving this financial problem effectively.
pixie
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Can anyone help me with this problem? I'm stuck

When will a payment of 300,000 galleons cancel Mr. Weasley’s liabilities to Gringott’s Bank of 100,000 galleons due after 2 years and 150,000 galleons due after 5 years if money is worth at an effective rate of 12%?
 
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pixie said:
When will a payment of 300,000 galleons cancel Mr. Weasley’s liabilities to Gringott’s Bank of 100,000 galleons due after 2 years and 150,000 galleons due after 5 years if money is worth at an effective rate of 12%?
HINT:
u = PV of the 100,000
v = PV of the 150,000
w = PV of the 300,000
w = u + v

You'll need to use logs:
remember that if a^p = x, then p = log(x) / log(a)
 
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