Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8670

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8670 – $5100 = $3570

Thus, Simple Interest = $3570

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3570}/_{5100 × 10}

= ³⁵⁷⁰⁰⁰/₅₁₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5100

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3570 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 10% of Principal

= 10% of $5100

= ¹⁰/₁₀₀ × 5100

= ^{10 × 5100}/₁₀₀

= ⁵¹⁰⁰⁰/₁₀₀ = 510

Thus, simple Interest for 1 year = $510

Now,

∵ If the simple Interest is $510, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₀ years

∴ If the simple Interest is $3570, then the time = ¹/₅₁₀ × 3570 years

= ^{1 × 3570}/₅₁₀ years

= ³⁵⁷⁰/₅₁₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.

(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?