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) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(3) 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.
(4) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.