Question:
Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
Correct Answer
$7810
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5500 ×6/100 × 7
= 5500 × 6 × 7/100
= 33000 × 7/100
= 231000/100
= $2310
Thus, Simple Interest = $2310
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 + $2310
= $7810
Thus, Amount to be paid = $7810 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 7)
= $5500 + ($5500 ×6/100 × 7)
= $5500 + (5500 × 6 × 7/100)
= $5500 + (33000 × 7/100)
= $5500 + (231000/100)
= $5500 + $2310 = $7810
Thus, Amount (A) to be paid = $7810 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5500, the simple interest in 1 year
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $330 × 7 = $2310
Thus, Simple Interest (SI) = $2310
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2310
= $7810
Thus, Amount to be paid = $7810 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(3) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(6) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(7) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(10) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.