Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
Correct Answer
$8313
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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) = $5100 × 7% × 9
= $5100 ×7/100 × 9
= 5100 × 7 × 9/100
= 35700 × 9/100
= 321300/100
= $3213
Thus, Simple Interest = $3213
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 = $5100 + $3213
= $8313
Thus, Amount to be paid = $8313 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 = $5100
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 7% × 9)
= $5100 + ($5100 ×7/100 × 9)
= $5100 + (5100 × 7 × 9/100)
= $5100 + (35700 × 9/100)
= $5100 + (321300/100)
= $5100 + $3213 = $8313
Thus, Amount (A) to be paid = $8313 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 $5100, the simple interest in 1 year
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $357 × 9 = $3213
Thus, Simple Interest (SI) = $3213
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3213
= $8313
Thus, Amount to be paid = $8313 Answer
Similar Questions
(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(6) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.