Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
Correct Answer
$7844
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5300 × 6% × 8
= $5300 ×6/100 × 8
= 5300 × 6 × 8/100
= 31800 × 8/100
= 254400/100
= $2544
Thus, Simple Interest = $2544
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2544
= $7844
Thus, Amount to be paid = $7844 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5300
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 6% × 8)
= $5300 + ($5300 ×6/100 × 8)
= $5300 + (5300 × 6 × 8/100)
= $5300 + (31800 × 8/100)
= $5300 + (254400/100)
= $5300 + $2544 = $7844
Thus, Amount (A) to be paid = $7844 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5300, the simple interest in 1 year
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = $318
Thus, simple interest for 1 year = $318
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $318 × 8 = $2544
Thus, Simple Interest (SI) = $2544
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2544
= $7844
Thus, Amount to be paid = $7844 Answer
Similar Questions
(1) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(6) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.