Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
Correct Answer
$8476
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5200 ×7/100 × 9
= 5200 × 7 × 9/100
= 36400 × 9/100
= 327600/100
= $3276
Thus, Simple Interest = $3276
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 + $3276
= $8476
Thus, Amount to be paid = $8476 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 7% × 9)
= $5200 + ($5200 ×7/100 × 9)
= $5200 + (5200 × 7 × 9/100)
= $5200 + (36400 × 9/100)
= $5200 + (327600/100)
= $5200 + $3276 = $8476
Thus, Amount (A) to be paid = $8476 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5200, the simple interest in 1 year
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = $364
Thus, simple interest for 1 year = $364
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $364 × 9 = $3276
Thus, Simple Interest (SI) = $3276
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3276
= $8476
Thus, Amount to be paid = $8476 Answer
Similar Questions
(1) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.
(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.