Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
Correct Answer
$8344
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5600 × 7% × 7
= $5600 ×7/100 × 7
= 5600 × 7 × 7/100
= 39200 × 7/100
= 274400/100
= $2744
Thus, Simple Interest = $2744
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 = $5600 + $2744
= $8344
Thus, Amount to be paid = $8344 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 = $5600
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 7)
= $5600 + ($5600 ×7/100 × 7)
= $5600 + (5600 × 7 × 7/100)
= $5600 + (39200 × 7/100)
= $5600 + (274400/100)
= $5600 + $2744 = $8344
Thus, Amount (A) to be paid = $8344 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 $5600, the simple interest in 1 year
= 7/100 × 5600
= 7 × 5600/100
= 39200/100 = $392
Thus, simple interest for 1 year = $392
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $392 × 7 = $2744
Thus, Simple Interest (SI) = $2744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2744
= $8344
Thus, Amount to be paid = $8344 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?