Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
Correct Answer
$8814
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 7% × 8
= $5650 ×7/100 × 8
= 5650 × 7 × 8/100
= 39550 × 8/100
= 316400/100
= $3164
Thus, Simple Interest = $3164
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 = $5650 + $3164
= $8814
Thus, Amount to be paid = $8814 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 = $5650
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 7% × 8)
= $5650 + ($5650 ×7/100 × 8)
= $5650 + (5650 × 7 × 8/100)
= $5650 + (39550 × 8/100)
= $5650 + (316400/100)
= $5650 + $3164 = $8814
Thus, Amount (A) to be paid = $8814 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 $5650, the simple interest in 1 year
= 7/100 × 5650
= 7 × 5650/100
= 39550/100 = $395.5
Thus, simple interest for 1 year = $395.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $395.5 × 8 = $3164
Thus, Simple Interest (SI) = $3164
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3164
= $8814
Thus, Amount to be paid = $8814 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
(4) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.