Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $10070

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 = $10070 – $5300 = $4770

Thus, Simple Interest = $4770

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 × 4770}/_{5300 × 10}

= ⁴⁷⁷⁰⁰⁰/₅₃₀₀₀

= 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) = $5300

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

Simple Interest = $4770 (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 $5300

= ¹⁰/₁₀₀ × 5300

= ^{10 × 5300}/₁₀₀

= ⁵³⁰⁰⁰/₁₀₀ = 530

Thus, simple Interest for 1 year = $530

Now,

∵ If the simple Interest is $530, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₀ years

∴ If the simple Interest is $4770, then the time = ¹/₅₃₀ × 4770 years

= ^{1 × 4770}/₅₃₀ years

= ⁴⁷⁷⁰/₅₃₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.

(3) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.

(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.

(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

(10) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.