Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

Correct Answer  $8855

Solution & Explanation

Solution

Given,

Principal (P) = $5750

Rate of Simple Interest (SI) = 6%

Time (t) = 9 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5750 × 6% × 9

= $5750 ×⁶/₁₀₀ × 9

= ^{5750 × 6 × 9}/₁₀₀

= ^{34500 × 9}/₁₀₀

= ³¹⁰⁵⁰⁰/₁₀₀

= $3105

Thus, Simple Interest = $3105

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 = $5750 + $3105

= $8855

Thus, Amount to be paid = $8855 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 = $5750

Rate of Simple Interest (SI) or (R) = 6%

And, Time (t) = 9 years

Thus, Amount (A)

= $5750 + ($5750 × 6% × 9)

= $5750 + ($5750 ×⁶/₁₀₀ × 9)

= $5750 + (^{5750 × 6 × 9}/₁₀₀)

= $5750 + (^{34500 × 9}/₁₀₀)

= $5750 + (³¹⁰⁵⁰⁰/₁₀₀)

= $5750 + $3105 = $8855

Thus, Amount (A) to be paid = $8855 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5750, the simple interest in 1 year

= ⁶/₁₀₀ × 5750

= ^{6 × 5750}/₁₀₀

= ³⁴⁵⁰⁰/₁₀₀ = $345

Thus, simple interest for 1 year = $345

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $345 × 9 = $3105

Thus, Simple Interest (SI) = $3105

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5750 + $3105

= $8855

Thus, Amount to be paid = $8855 Answer

Similar Questions

(1) 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.

(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(3) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?

(6) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.

(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.