Question

Reggie takes a loan for 5 years to be repaid by level end of year payments of R. The interest paid in the third payment was 136.16 and the interest paid in the 5^th payment was 47.62. Please find the amount of principal paid in the fourth payment P₄.

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Answer 1

the entire loan of A amount will be paid back in (P + interest) form in 5 years. Initial years, Higher will be the interest and lower will be the principal.

we use the formula of compund interest to calculate the rate of interest where, CI= P[(1+r/100)^n - 1] where, CI is compound interest, r= rate of interest and n= number of years. P= principal.

for 3rd year, according to the equation,

136.15= P[(1=r/100)^3 - 1]........(1)

for 5th year,

47.62= P [(1+r/100)^5 - 1]..........(2)

Dividing equation (I) and (2), we get

2.86= [(1+r/100)^3 - 1] / [(1+r/100)^5 -1]

which results to,

[(1+r/100)^5] - [(1+r/100)^3] = 0.65

Using trial and error method we get, r= 18%

Now, for 5th yr interest is 47.62

for 4th year interest = x

for 3rd year interest = 136.15

using proportion formula of a:b :: b:c

136.16/x = x/ 47.62

x= 80.52 (3rd year interest CI)

now using value of x, i.e. CI= P [ 1.18^4 - 1]

P= 85.66 ( principal for 4th year) Answer