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When Grace was born in 2007, her parents deposited $10000 into an investment account with an annual interest rate of 5%, compounded quarterly.
Calculate the amount of money in her account when she turns 18.
Once she turns 18, Grace begins depositing $400 into the same account at the end of each month.
Determine the first year in which Grace will have more than $200000 in her account.
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Lucia, an aspiring culinary celebrity, takes out a loan from her bank to purchase equipment for her bakery. The bank agrees to lend her $100,000 at an interest rate of 6% compounded monthly.
The bank requires equal monthly repayments of $R for 10 years.
Calculate the value of $R to two decimal places.
For the first three years, Lucia makes all her payments on time. At this point she receives a large inheritance and decides to clear the remaining debt with one final lump-sum payment of $X.
Determine the value of $X to two decimal places.
Find the amount of interest Lucia saves by making her lump-sum payment at the end of year 3 instead of paying off the loan over 10 years.
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A line segment of 6m is divided into an infinite number of smaller segments. The segments form a geometric sequence with segment lengths k, k2, k3…
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Find the value of k.
An infinite sequence of squares with side lengths k, k2, k3… are arranged side by side on the x-axis starting at the origin.
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Find the combined area of all the squares.
The line L passes through all the squares, dividing them into 2 regions of equal area.
Find the equation of L in the form y=mx+c.
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