Question 1132297: John joined the wazalendo saving and credit society and agree to contribute share of Tsh,1600000 at the end of each year from a salary. Find
(a). The value of this fund at the end of 5 years and.
(b). The present value of the money after period of installments if money is worth 6% per annum compound interest
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the investment is 1.6 million tanzanian shillings at the end of each year for 5 years.
the interest rate is 6% per year.
there are several ways to solve this, the easiest being to use a financial calculator.
there are also formulas that i will give to you.
lastly, you can solve it the hard way by doing it manually.
this is not recommended but available when the number of calculations is not overly large.
first the use of a calculator.
the online calculator i used can be found at https://arachnoid.com/finance/
your total investment is 1.6 million at the end of each year for 5 years.
this is equal to 5 * 1.6 = 8 million = 8,000,000
the present value is calculated by making the following inputs to the calculator.
present value = 0
future value = 0
payment at the end of each time period = -1600000
interest rate percent for each time period = 6%.
number of time periods = 5
you then click on pv and it tell you that the present value is 6,739,782.06 tanzanian shillings.
here's what it looks like.
the future value is calculated by making the following inputs to the calculator.
present value = 0
future value = 0
payment at the end of each time period = -1600000
interest rate percent for each time period = 6%.
number of time periods = 5
you then click on fv and it tell you that the present value is 9,019,348.74 tanzanian shillings.
here's what it looks like.
there is a formula you can use that should give you the same answer.
that formula can be found in the following reference:
https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#notes
the formula to be used for the present value is:
PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
p = (a*(1-1/(1+r)^n))/r
p is the present value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods.
the formula to be used for the future value is:
FUTURE VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
f = (a*((1+r)^n-1))/r
f is the future value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods
you would enter the appropriate values into your calculator exactly as shown and you should get the same answer that the calculator gave you after rounding to 2 decimal places.
for the present value, your entries to the calculator will be:
(1600000*(1-1/(1+.06)^5))/.06
the calculator will tell you that the present value is equal to 6739782.057 which is rounded to 6739782.06 which is equal to 6,739,782.06 after commas are included.
this agrees with what the calculator told you.
for the future value, your entries to the calculator will be:
(1600000*((1+.06)^5-1))/.06
the calculator will tell you that the future value is equal to 9019348.736 which is rounded to 9019348.74 which is equal to 9,019,348.74 after commas are included.
lastly, you can do the calculator manually through the use of your calculator.
you essentially have 5 investments in each time period.
your time periods are from time period 0 to time period 5.
time period 1 is the end of year 1.
time period 2 is the end of year 2.
etc.
to find the total investment, you add up the investments in each time period.
to find the present value, you divide each time period investment by 1.06 raised to the power of the time period.
investment in time period 1 is divided by 1.06.
investment in time period 2 is divided by 1.06 ^ 2.
etc.
to find the future fvalue, you multiply each time period investment by 1.06 raised to the power of 5 minus the time period.
investment in time period 1 is multiplied by 1.06 ^ (5 - 1)
investment in time period 2 is multiplied by 1.06 ^ (5 - 2)
...
investment in time period 5 is multiplied by 1.06 ^ (5 - 5)
the following excel printout shows the calculations.
when working with the calculator, you use the percent interest rate.
when working with the formulas, you use the interest rate.
interest rate = percent interest rate / 100.
when working with the calculator, investments are negative because they're money going out.
what you get back is positive because it's money coming in.
the calculator will automatically make the present and future value negative if the payments are positive, and vice versa.
the value of the fund at the end of the investment period is the future value of the payments at 6% per year.
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