Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
Correct Answer
$9350
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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) = $5500 × 7% × 10
= $5500 ×7/100 × 10
= 5500 × 7 × 10/100
= 38500 × 10/100
= 385000/100
= $3850
Thus, Simple Interest = $3850
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 = $5500 + $3850
= $9350
Thus, Amount to be paid = $9350 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 = $5500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 7% × 10)
= $5500 + ($5500 ×7/100 × 10)
= $5500 + (5500 × 7 × 10/100)
= $5500 + (38500 × 10/100)
= $5500 + (385000/100)
= $5500 + $3850 = $9350
Thus, Amount (A) to be paid = $9350 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 $5500, the simple interest in 1 year
= 7/100 × 5500
= 7 × 5500/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $385 × 10 = $3850
Thus, Simple Interest (SI) = $3850
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3850
= $9350
Thus, Amount to be paid = $9350 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(2) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(3) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(5) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(8) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.