Question:
Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
Correct Answer
$8112
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5200 ×7/100 × 8
= 5200 × 7 × 8/100
= 36400 × 8/100
= 291200/100
= $2912
Thus, Simple Interest = $2912
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 + $2912
= $8112
Thus, Amount to be paid = $8112 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) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 7% × 8)
= $5200 + ($5200 ×7/100 × 8)
= $5200 + (5200 × 7 × 8/100)
= $5200 + (36400 × 8/100)
= $5200 + (291200/100)
= $5200 + $2912 = $8112
Thus, Amount (A) to be paid = $8112 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 8 years
= Simple interest for 1 year × 8
= $364 × 8 = $2912
Thus, Simple Interest (SI) = $2912
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2912
= $8112
Thus, Amount to be paid = $8112 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(2) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
(3) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(5) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(8) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.