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) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(6) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(9) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.