Question

Peter borrowed a sum of R12 850.00 at the beginning of a year with a certain simple interest rate. After 14 quarters, in a different loan, he borrowed an extra sum of R3 273.00, but at the simple interest half the former. At the end of four years, Peter paid a simple interest amount of R1 980.00 for both the loans. The original annual simple interest rate, rounded to two decimal places, is?​

Answer 1

The original annual simple interest rate, rounded to two decimal places, is 3.79%

What is the formula for simple interest?

The simple interest on a loan or deposit is determined as the principal multiplied by the simple interest rate and time

I=PRT

The first loan:

P=12 850.00

R=r(assume it is r)

T=4 years

I=12 850.00*r*4

I=51400r

The second loan was taken after 14 quarters the first was taken out, which is the same as after 3.5 years, hence, the interest on the second loan is only for a half a year

P=3 273.00

R=0.5r( half of the interest on the first loan)

T=0.5 years

I=3 273.00*0.5r*0.5

I= 818.25r

Total interest=51400r+818.25r

Total interest=52218.25r

total interest paid=1 980.00

1 980.00=52218.25r

r=1 980.00/52218.25

r=3.79%

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