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) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.
(3) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(5) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(7) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(10) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.