Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 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) = 9% per annum

Amount (A) = $10317

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 = $10317 – $5700 = $4617

Thus, Simple Interest = $4617

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 × 4617}/_{5700 × 9}

= ⁴⁶¹⁷⁰⁰/₅₁₃₀₀

= 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) = 9% per annum

Simple Interest = $4617 (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 = 9% of Principal

= 9% of $5700

= ⁹/₁₀₀ × 5700

= ^{9 × 5700}/₁₀₀

= ⁵¹³⁰⁰/₁₀₀ = 513

Thus, simple Interest for 1 year = $513

Now,

∵ If the simple Interest is $513, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₃ years

∴ If the simple Interest is $4617, then the time = ¹/₅₁₃ × 4617 years

= ^{1 × 4617}/₅₁₃ years

= ⁴⁶¹⁷/₅₁₃ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(2) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

(4) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(6) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

(9) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?