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) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(8) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.