Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $10830

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 = $10830 – $5700 = $5130

Thus, Simple Interest = $5130

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 × 5130}/_{5700 × 10}

= ⁵¹³⁰⁰⁰/₅₇₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5700

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

Simple Interest = $5130 (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 $5700

= ¹⁰/₁₀₀ × 5700

= ^{10 × 5700}/₁₀₀

= ⁵⁷⁰⁰⁰/₁₀₀ = 570

Thus, simple Interest for 1 year = $570

Now,

∵ If the simple Interest is $570, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₇₀ years

∴ If the simple Interest is $5130, then the time = ¹/₅₇₀ × 5130 years

= ^{1 × 5130}/₅₇₀ years

= ⁵¹³⁰/₅₇₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.

(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(3) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(10) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?