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 $10600 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $10600

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 = $10600 – $5300 = $5300

Thus, Simple Interest = $5300

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 × 5300}/_{5300 × 10}

= ⁵³⁰⁰⁰⁰/₅₃₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $5300 (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 $5300, then the time = ¹/₅₃₀ × 5300 years

= ^{1 × 5300}/₅₃₀ years

= ⁵³⁰⁰/₅₃₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.

(2) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?

(9) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?