Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.
Correct Answer
$7878
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5050 ×8/100 × 7
= 5050 × 8 × 7/100
= 40400 × 7/100
= 282800/100
= $2828
Thus, Simple Interest = $2828
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 + $2828
= $7878
Thus, Amount to be paid = $7878 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 8% × 7)
= $5050 + ($5050 ×8/100 × 7)
= $5050 + (5050 × 8 × 7/100)
= $5050 + (40400 × 7/100)
= $5050 + (282800/100)
= $5050 + $2828 = $7878
Thus, Amount (A) to be paid = $7878 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5050, the simple interest in 1 year
= 8/100 × 5050
= 8 × 5050/100
= 40400/100 = $404
Thus, simple interest for 1 year = $404
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $404 × 7 = $2828
Thus, Simple Interest (SI) = $2828
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2828
= $7878
Thus, Amount to be paid = $7878 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(3) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(5) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(7) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(9) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.