Question : Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
Correct Answer $6655
Solution & Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7
= $5500 ×3/100 × 7
= 5500 × 3 × 7/100
= 16500 × 7/100
= 115500/100
= $1155
Thus, Simple Interest = $1155
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 + $1155
= $6655
Thus, Amount to be paid = $6655 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 7)
= $5500 + ($5500 ×3/100 × 7)
= $5500 + (5500 × 3 × 7/100)
= $5500 + (16500 × 7/100)
= $5500 + (115500/100)
= $5500 + $1155 = $6655
Thus, Amount (A) to be paid = $6655 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5500, the simple interest in 1 year
= 3/100 × 5500
= 3 × 5500/100
= 16500/100 = $165
Thus, simple interest for 1 year = $165
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $165 × 7 = $1155
Thus, Simple Interest (SI) = $1155
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1155
= $6655
Thus, Amount to be paid = $6655 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.