Question:
Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
Correct Answer
$7280
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5200 ×5/100 × 8
= 5200 × 5 × 8/100
= 26000 × 8/100
= 208000/100
= $2080
Thus, Simple Interest = $2080
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 + $2080
= $7280
Thus, Amount to be paid = $7280 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 8)
= $5200 + ($5200 ×5/100 × 8)
= $5200 + (5200 × 5 × 8/100)
= $5200 + (26000 × 8/100)
= $5200 + (208000/100)
= $5200 + $2080 = $7280
Thus, Amount (A) to be paid = $7280 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $260 × 8 = $2080
Thus, Simple Interest (SI) = $2080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2080
= $7280
Thus, Amount to be paid = $7280 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(6) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?