SOLUTION: a loan is repaid with equal payments of 200 dollar at the end of each week for 15 years .if interest is 10.4% p.a. compounded weekly and assuming that there are 52 weeks in a year,

Question 1098670: a loan is repaid with equal payments of 200 dollar at the end of each week for 15 years .if interest is 10.4% p.a. compounded weekly and assuming that there are 52 weeks in a year,
(a) the total amount repaid,
(b) the present value of the loan (correct to 2 decimal places),
(c) the total amount of interest paid (correct to 2 decimal places).

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
payments are 200 dollars at the end of each week for 15 years.
interest rate is 10.4% per year compounded weekly.
assuming 52 weeks in a year, you would translate this problem as follows for the online calculator at

present value = 0
future value = 0
number of periods = 15 * 52 = 780 weeks
payment amount = -200
interest rate % per period = 10.4 / 52 = .2
payment made at end of time period

you would then click on PV and the calculator will tell you that the present value of the loan is $78,953.63

the total payments you made would be 780 * $200 = $156,000

the total interest you paid would be $156,000 - $78,953.63 = $77,046.37

the calculator i used is at https://arachnoid.com/finance/

here's a picture of the results from this calculator.

$$$

you could also have calculated manually using the following formula.

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.

in your problem:

a = 200
r = 10.4 / 100 = .104 / 52 = .002
n = 15 * 52 = 780

the formula of p = (a*(1-1/(1+r)^n))/r becomes:

p = (200*(1-1/(1.002)^780))/.002

the result would be p = $78,953.62978 which is equal to $78,953.63 rounded to 2 decimal places.

that's the same result that the calculator gave you.

a summary of financial formulas that you might find useful can be found at this link.

https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f5

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