Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
Correct Answer
$9605
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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% × 10
= $5650 ×7/100 × 10
= 5650 × 7 × 10/100
= 39550 × 10/100
= 395500/100
= $3955
Thus, Simple Interest = $3955
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 + $3955
= $9605
Thus, Amount to be paid = $9605 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) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 7% × 10)
= $5650 + ($5650 ×7/100 × 10)
= $5650 + (5650 × 7 × 10/100)
= $5650 + (39550 × 10/100)
= $5650 + (395500/100)
= $5650 + $3955 = $9605
Thus, Amount (A) to be paid = $9605 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 10 years
= Simple interest for 1 year × 10
= $395.5 × 10 = $3955
Thus, Simple Interest (SI) = $3955
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3955
= $9605
Thus, Amount to be paid = $9605 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(6) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.