document.write( "Question 1157860: Justine invested R45000 at the beginning of 2014. The interest rate is 3.5%p.a. After 2 years, the interest rate increases with 2%p.a. What will her final amount be at the end of 2020? (Could I get a step by step explanation please, thanks in advance) \n" ); document.write( "
Algebra.Com's Answer #780753 by Theo(13342)\"\" \"About 
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the formula to use is f = p * (1 + r) ^ n
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the present value
\n" ); document.write( "r is the interest rate per time period.
\n" ); document.write( "n is the number of time periods.\r
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\n" ); document.write( "\n" ); document.write( "in your problem, you have two formulas.
\n" ); document.write( "one for the first 2 years.
\n" ); document.write( "one for the remaining years.\r
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\n" ); document.write( "\n" ); document.write( "the investment is at the beginning of 2014.
\n" ); document.write( "the interest rate is 3.5% per year for two years.
\n" ); document.write( "the formula for the first 2 years is f = 45000 * (1 + .035) ^ 2
\n" ); document.write( "solve for f to get f = 48205.125
\n" ); document.write( "that's at the end of the second year, which is the end of 2015.
\n" ); document.write( "the end of the second year is also assumed to be the beginning of the third year.
\n" ); document.write( "end of 2015 is therefore the beginning of 2016.
\n" ); document.write( "from the end of 2015 to the end of 2020 is 5 years.
\n" ); document.write( "the future value at the end of 2015 becomes the present value at the beginning of 2016.
\n" ); document.write( "it's the same time point.
\n" ); document.write( "the formula from the beginning of 2016 to the end of 2020 bcomes f = 48205.125 * (1 + .055) ^ 5.
\n" ); document.write( "the interest rate becomes 2% greater than 3.5%.
\n" ); document.write( "this makes is 5.5% which is the same as .055.
\n" ); document.write( "solve for f to get f = 63002.17048.
\n" ); document.write( "that's the amount justine has at the end of 2020.
\n" ); document.write( "note the concept of time points.
\n" ); document.write( "time point 0 is the beginning of 2014.
\n" ); document.write( "time point 1 is the end of 2014 and the beginning of 2015.
\n" ); document.write( "time point 2 is the end of 2015 and the beginning of 2016.
\n" ); document.write( "time point 3 is the end of 2016 and the beginning of 2017.
\n" ); document.write( "time point 4 is the end of 2017 and the beginning of 2018.
\n" ); document.write( "time point 5 is the end of 2018 and the beginning of 2019.
\n" ); document.write( "time point 6 is the end of 2019 and the beginning of 2020.
\n" ); document.write( "time point 7 is the end of 2020 and the beginning of 2021.
\n" ); document.write( "note that when you calculate number of years, you have to be consistent.
\n" ); document.write( "beginning of 2014 is the same as the end of 2013.
\n" ); document.write( "end of 2013 to end of 2015 is 2 years.
\n" ); document.write( "beginning of 2016 is the same as the end of 2015.
\n" ); document.write( "end of 2015 to end of 2020 is 5 years.
\n" ); document.write( "the following excel sheet printout shows the year by year calculation, based on my understanding of your problem.
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