MHB Compounding Interest: Confirm my answers?

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The discussion focuses on confirming calculations for compound interest problems using the formulas for future value (A) and present value (P). The user provided answers for four scenarios involving different principal amounts, interest rates, time periods, and compounding frequencies. Calculations were presented, showing that the first scenario's answer was slightly off, while the other answers for present values and future values were confirmed to be accurate. The formulas used were correctly applied, demonstrating a solid understanding of compound interest calculations. Overall, the user's answers were mostly correct, with minor adjustments needed for the first scenario.
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Find the missing information:

1) P = 3800, r = 8%, t = 39 months, c = quarterly, A = ?
2) P = ?, r = 7.5%, t = 2 years, c = monthly, A = 5,000
3) P = ?, r = 5.2%, t = 3 years, c = weekly, A = 3000
4) P = 3723, r = 6.75%, t = 30 months, c = semi annually, A = ?

My answers were:
1) A = 4912
2) P = 4306
3) P = 2566
4) A = 4395

Can someone confirm that my answers are correct? (you don't have to do all of them, but it would be really helpful! Also it said P or PV and A or FV in the question - I just wrote P and A)
 
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The formula we may begin with is:

$$A=P\left(1+\frac{r}{n}\right)^{nt}$$

the other form we will need is:

$$P=A\left(1+\frac{r}{n}\right)^{-nt}$$

1.) $$A=3800\left(1+\frac{0.08}{4}\right)^{4\cdot3.25}\approx4915.71$$

2.) $$P=5000\left(1+\frac{0.075}{12}\right)^{-12\cdot2}\approx4305.55$$

3.) $$P=3000\left(1+\frac{0.052}{52}\right)^{-52\cdot3}\approx2566.88$$

4.) $$A=3723\left(1+\frac{0.0675}{2}\right)^{2\cdot2.5}\approx4395.12$$
 
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