Question:
Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
Correct Answer
$7696
Solution And Explanation
Solution
Given,
Principal (P) = $5200
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) = $5200 × 6% × 8
= $5200 ×6/100 × 8
= 5200 × 6 × 8/100
= 31200 × 8/100
= 249600/100
= $2496
Thus, Simple Interest = $2496
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 = $5200 + $2496
= $7696
Thus, Amount to be paid = $7696 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 = $5200
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 6% × 8)
= $5200 + ($5200 ×6/100 × 8)
= $5200 + (5200 × 6 × 8/100)
= $5200 + (31200 × 8/100)
= $5200 + (249600/100)
= $5200 + $2496 = $7696
Thus, Amount (A) to be paid = $7696 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 $5200, the simple interest in 1 year
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $312 × 8 = $2496
Thus, Simple Interest (SI) = $2496
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2496
= $7696
Thus, Amount to be paid = $7696 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(4) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(6) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(8) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?