Question #306621

A loan will be paid by means of payment of 250 each,every 6 months for 10 years.An interest rate of 5% per year compounded every 6 months will be applicable the present value of the loan is


1
Expert's answer
2022-03-07T21:51:01-0500

Solution


Consider,


AA – The payment per period.


PP – The principal amount (loan taken).


rr – The interest rate per year,


nn – The number of times, the amount is compounded per annum, and


tt – The number of years,


we can write the formula, as 


P=A×(1+rn)nt1(rn)(1+rn)nt{\color{Blue} P=A\times\frac{(1+\frac{r}{n})^{nt}-1}{(\frac{r}{n})(1+\frac{r}{n})^{nt}}}


Replacing the values,


A=250A = 250 ,        r=5%r = 5\% ,            n=2n = 2 (compounded every six months), t=10t = 10 years


P=(250)×(1+0.052)(2)(10)1(0.052)(1+0.052)(2)(10){\color{Red} P=(250)\times\frac{(1+\frac{0.05}{2})^{(2)(10)}-1}{(\frac{0.05}{2})(1+\frac{0.05}{2})^{(2)(10)}}}


P=3897.290572\


Hence the loan amount to be paid will be


P=3897.290572\






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