Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
Correct Answer
$8865.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5950 × 7% × 7
= $5950 ×7/100 × 7
= 5950 × 7 × 7/100
= 41650 × 7/100
= 291550/100
= $2915.5
Thus, Simple Interest = $2915.5
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 = $5950 + $2915.5
= $8865.5
Thus, Amount to be paid = $8865.5 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 = $5950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 7)
= $5950 + ($5950 ×7/100 × 7)
= $5950 + (5950 × 7 × 7/100)
= $5950 + (41650 × 7/100)
= $5950 + (291550/100)
= $5950 + $2915.5 = $8865.5
Thus, Amount (A) to be paid = $8865.5 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 $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $416.5 × 7 = $2915.5
Thus, Simple Interest (SI) = $2915.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2915.5
= $8865.5
Thus, Amount to be paid = $8865.5 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(4) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(6) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(10) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.