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 And 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) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(6) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(7) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?