MHB Given amount and interest rate, find principal

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To determine the principal needed to reach $60,000 in 8 years at a 9% interest rate, the formula used is 60000/((1 + .09/f)^(8*f)), where 'f' represents the compounding frequency. The discussion emphasizes the importance of knowing whether the interest is simple or compounded, as well as the specific compounding period. Participants seek clarification on these details to accurately calculate the required deposit. The conversation centers around the mathematical approach to solving the problem. Understanding the compounding method is crucial for obtaining the correct principal amount.
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Homework help please: If I want to have $60,000 in 8 years, how much would I need to deposit in the bank today if the account pays an interest rate of 9%?
 
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Re: Please help me

brownrebecca333 said:
Homework help please: If I want to have $60,000 in 8 years, how much would I need to deposit in the bank today if the account pays an interest rate of 9%?

Simple or compounded interest? If compounded, what is the compounding period?
 
brownrebecca333 said:
Homework help please: If I want to have $60,000 in 8 years, how much would I need to deposit in the bank today if the account pays an interest rate of 9%?
60000/((1 + .09/f)^(8*f)) where f = compounding frequency
 
There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...

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