Question:
Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
Correct Answer
$9360
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5200 ×10/100 × 8
= 5200 × 10 × 8/100
= 52000 × 8/100
= 416000/100
= $4160
Thus, Simple Interest = $4160
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 + $4160
= $9360
Thus, Amount to be paid = $9360 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 10% × 8)
= $5200 + ($5200 ×10/100 × 8)
= $5200 + (5200 × 10 × 8/100)
= $5200 + (52000 × 8/100)
= $5200 + (416000/100)
= $5200 + $4160 = $9360
Thus, Amount (A) to be paid = $9360 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5200, the simple interest in 1 year
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = $520
Thus, simple interest for 1 year = $520
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $520 × 8 = $4160
Thus, Simple Interest (SI) = $4160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $4160
= $9360
Thus, Amount to be paid = $9360 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(8) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.