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) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(2) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.