Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
Correct Answer
$6110.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 3% × 7
= $5050 ×3/100 × 7
= 5050 × 3 × 7/100
= 15150 × 7/100
= 106050/100
= $1060.5
Thus, Simple Interest = $1060.5
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 = $5050 + $1060.5
= $6110.5
Thus, Amount to be paid = $6110.5 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 = $5050
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 3% × 7)
= $5050 + ($5050 ×3/100 × 7)
= $5050 + (5050 × 3 × 7/100)
= $5050 + (15150 × 7/100)
= $5050 + (106050/100)
= $5050 + $1060.5 = $6110.5
Thus, Amount (A) to be paid = $6110.5 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 $5050, the simple interest in 1 year
= 3/100 × 5050
= 3 × 5050/100
= 15150/100 = $151.5
Thus, simple interest for 1 year = $151.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $151.5 × 7 = $1060.5
Thus, Simple Interest (SI) = $1060.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1060.5
= $6110.5
Thus, Amount to be paid = $6110.5 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(8) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(10) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.