Simple Interest
Math MCQs

Question :    Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.

Correct Answer  $9126

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 8%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5850 × 8% × 7

= $5850 ×⁸/₁₀₀ × 7

= ^{5850 × 8 × 7}/₁₀₀

= ^{46800 × 7}/₁₀₀

= ³²⁷⁶⁰⁰/₁₀₀

= $3276

Thus, Simple Interest = $3276

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 = $5850 + $3276

= $9126

Thus, Amount to be paid = $9126 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 = $5850

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 7 years

Thus, Amount (A)

= $5850 + ($5850 × 8% × 7)

= $5850 + ($5850 ×⁸/₁₀₀ × 7)

= $5850 + (^{5850 × 8 × 7}/₁₀₀)

= $5850 + (^{46800 × 7}/₁₀₀)

= $5850 + (³²⁷⁶⁰⁰/₁₀₀)

= $5850 + $3276 = $9126

Thus, Amount (A) to be paid = $9126 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5850, the simple interest in 1 year

= ⁸/₁₀₀ × 5850

= ^{8 × 5850}/₁₀₀

= ⁴⁶⁸⁰⁰/₁₀₀ = $468

Thus, simple interest for 1 year = $468

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $468 × 7 = $3276

Thus, Simple Interest (SI) = $3276

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $3276

= $9126

Thus, Amount to be paid = $9126 Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.

(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(5) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.