Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
Correct Answer
$8965
Solution And Explanation
Solution
Given,
Principal (P) = $5500
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) = $5500 × 7% × 9
= $5500 ×7/100 × 9
= 5500 × 7 × 9/100
= 38500 × 9/100
= 346500/100
= $3465
Thus, Simple Interest = $3465
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 + $3465
= $8965
Thus, Amount to be paid = $8965 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) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 7% × 9)
= $5500 + ($5500 ×7/100 × 9)
= $5500 + (5500 × 7 × 9/100)
= $5500 + (38500 × 9/100)
= $5500 + (346500/100)
= $5500 + $3465 = $8965
Thus, Amount (A) to be paid = $8965 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 9 years
= Simple interest for 1 year × 9
= $385 × 9 = $3465
Thus, Simple Interest (SI) = $3465
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3465
= $8965
Thus, Amount to be paid = $8965 Answer
Similar Questions
(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(5) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 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 10% simple interest for 7 years.
(10) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.