Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
Correct Answer
$8736
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5600 ×7/100 × 8
= 5600 × 7 × 8/100
= 39200 × 8/100
= 313600/100
= $3136
Thus, Simple Interest = $3136
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 + $3136
= $8736
Thus, Amount to be paid = $8736 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 8)
= $5600 + ($5600 ×7/100 × 8)
= $5600 + (5600 × 7 × 8/100)
= $5600 + (39200 × 8/100)
= $5600 + (313600/100)
= $5600 + $3136 = $8736
Thus, Amount (A) to be paid = $8736 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5600, the simple interest in 1 year
= 7/100 × 5600
= 7 × 5600/100
= 39200/100 = $392
Thus, simple interest for 1 year = $392
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $392 × 8 = $3136
Thus, Simple Interest (SI) = $3136
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $3136
= $8736
Thus, Amount to be paid = $8736 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(4) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.