Question

The Meek brothers are planning a trip around the world. They hope to work some as they go, but
believe that they should have accessible $800 per month so they can live in relative comfort for the year
they plan to be gone. How much should they have in an account earning 6% compounded monthly
when they leave so that they can withdraw the desired $800 each month for twelve months?

Answer 1

Answer on Question #51037 – Math - Algebra

Question

The Meek brothers are planning a trip around the world. They hope to work some as they go, but believe that they should have accessible $800 per month so they can live in relative comfort for the year

they plan to be gone. How much should they have in an account earning 6% compounded monthly when they leave so that they can withdraw the desired $800 each month for twelve months?

Solution

Consider two cases.

The first case. Apply compound interest formula.

If they have $y$ dollars in an account compounded monthly, then $y(1 + 0.06)^{12} \geq 800 \cdot 12$, hence $y \geq \frac{800 \cdot 12}{(1 + 0.06)^{12}}$, which is equivalent to $y \geq \$4771$ (in this case account can be used with deductions).

The second case. If Meek brothers want to have 800 dollars a month, then 800 dollars must be a $6\%$ of sum in account.

Construct a proportion:

$$800 - 0.06$$ $$x - 1$$ $$x = \frac{800}{0.06} = 13333. (33);$$

So they should have at least $13 333.34$ (in this case account can be used without deductions, all withdrawn money will be added by means of interest).

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