SOLUTION: 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 2
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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) Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the formula to use is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
in your problem, you have two formulas.
one for the first 2 years.
one for the remaining years.
the investment is at the beginning of 2014.
the interest rate is 3.5% per year for two years.
the formula for the first 2 years is f = 45000 * (1 + .035) ^ 2
solve for f to get f = 48205.125
that's at the end of the second year, which is the end of 2015.
the end of the second year is also assumed to be the beginning of the third year.
end of 2015 is therefore the beginning of 2016.
from the end of 2015 to the end of 2020 is 5 years.
the future value at the end of 2015 becomes the present value at the beginning of 2016.
it's the same time point.
the formula from the beginning of 2016 to the end of 2020 bcomes f = 48205.125 * (1 + .055) ^ 5.
the interest rate becomes 2% greater than 3.5%.
this makes is 5.5% which is the same as .055.
solve for f to get f = 63002.17048.
that's the amount justine has at the end of 2020.
note the concept of time points.
time point 0 is the beginning of 2014.
time point 1 is the end of 2014 and the beginning of 2015.
time point 2 is the end of 2015 and the beginning of 2016.
time point 3 is the end of 2016 and the beginning of 2017.
time point 4 is the end of 2017 and the beginning of 2018.
time point 5 is the end of 2018 and the beginning of 2019.
time point 6 is the end of 2019 and the beginning of 2020.
time point 7 is the end of 2020 and the beginning of 2021.
note that when you calculate number of years, you have to be consistent.
beginning of 2014 is the same as the end of 2013.
end of 2013 to end of 2015 is 2 years.
beginning of 2016 is the same as the end of 2015.
end of 2015 to end of 2020 is 5 years.
the following excel sheet printout shows the year by year calculation, based on my understanding of your problem.
