Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

Correct Answer  $8240

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 6%

Time (t) = 10 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) = $5150 × 6% × 10

= $5150 ×⁶/₁₀₀ × 10

= ^{5150 × 6 × 10}/₁₀₀

= ^{30900 × 10}/₁₀₀

= ³⁰⁹⁰⁰⁰/₁₀₀

= $3090

Thus, Simple Interest = $3090

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 = $5150 + $3090

= $8240

Thus, Amount to be paid = $8240 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 = $5150

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

And, Time (t) = 10 years

Thus, Amount (A)

= $5150 + ($5150 × 6% × 10)

= $5150 + ($5150 ×⁶/₁₀₀ × 10)

= $5150 + (^{5150 × 6 × 10}/₁₀₀)

= $5150 + (^{30900 × 10}/₁₀₀)

= $5150 + (³⁰⁹⁰⁰⁰/₁₀₀)

= $5150 + $3090 = $8240

Thus, Amount (A) to be paid = $8240 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 $5150, the simple interest in 1 year

= ⁶/₁₀₀ × 5150

= ^{6 × 5150}/₁₀₀

= ³⁰⁹⁰⁰/₁₀₀ = $309

Thus, simple interest for 1 year = $309

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $309 × 10 = $3090

Thus, Simple Interest (SI) = $3090

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $3090

= $8240

Thus, Amount to be paid = $8240 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?

(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.

(6) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.

(7) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.