Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
Correct Answer
$10260
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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) = $5700 × 8% × 10
= $5700 ×8/100 × 10
= 5700 × 8 × 10/100
= 45600 × 10/100
= 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) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 8% × 10)
= $5700 + ($5700 ×8/100 × 10)
= $5700 + (5700 × 8 × 10/100)
= $5700 + (45600 × 10/100)
= $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 = 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 $5700, the simple interest in 1 year
= 8/100 × 5700
= 8 × 5700/100
= 45600/100 = $456
Thus, simple interest for 1 year = $456
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $456 × 10 = $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 Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(2) 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.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(8) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(10) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.