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) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(6) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(10) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?