Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
Correct Answer
$10260
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5700 × 10% × 8
= $5700 ×10/100 × 8
= 5700 × 10 × 8/100
= 57000 × 8/100
= 456000/100
= $4560
Thus, Simple Interest = $4560
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 = $5700 + $4560
= $10260
Thus, Amount to be paid = $10260 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 = $5700
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 10% × 8)
= $5700 + ($5700 ×10/100 × 8)
= $5700 + (5700 × 10 × 8/100)
= $5700 + (57000 × 8/100)
= $5700 + (456000/100)
= $5700 + $4560 = $10260
Thus, Amount (A) to be paid = $10260 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5700, the simple interest in 1 year
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = $570
Thus, simple interest for 1 year = $570
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $570 × 8 = $4560
Thus, Simple Interest (SI) = $4560
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $4560
= $10260
Thus, Amount to be paid = $10260 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(9) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?