Question:
Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
Correct Answer
$6448
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5200 ×3/100 × 8
= 5200 × 3 × 8/100
= 15600 × 8/100
= 124800/100
= $1248
Thus, Simple Interest = $1248
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 + $1248
= $6448
Thus, Amount to be paid = $6448 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 3% × 8)
= $5200 + ($5200 ×3/100 × 8)
= $5200 + (5200 × 3 × 8/100)
= $5200 + (15600 × 8/100)
= $5200 + (124800/100)
= $5200 + $1248 = $6448
Thus, Amount (A) to be paid = $6448 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5200, the simple interest in 1 year
= 3/100 × 5200
= 3 × 5200/100
= 15600/100 = $156
Thus, simple interest for 1 year = $156
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $156 × 8 = $1248
Thus, Simple Interest (SI) = $1248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1248
= $6448
Thus, Amount to be paid = $6448 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(2) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.