Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
Correct Answer
$7560
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5600 × 5% × 7
= $5600 ×5/100 × 7
= 5600 × 5 × 7/100
= 28000 × 7/100
= 196000/100
= $1960
Thus, Simple Interest = $1960
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 = $5600 + $1960
= $7560
Thus, Amount to be paid = $7560 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 = $5600
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5600 + ($5600 × 5% × 7)
= $5600 + ($5600 ×5/100 × 7)
= $5600 + (5600 × 5 × 7/100)
= $5600 + (28000 × 7/100)
= $5600 + (196000/100)
= $5600 + $1960 = $7560
Thus, Amount (A) to be paid = $7560 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5600, the simple interest in 1 year
= 5/100 × 5600
= 5 × 5600/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $280 × 7 = $1960
Thus, Simple Interest (SI) = $1960
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $1960
= $7560
Thus, Amount to be paid = $7560 Answer
Similar Questions
(1) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(7) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(9) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?