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) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(3) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(5) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(6) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(10) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.