Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8639

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 = $8639 – $5300 = $3339

Thus, Simple Interest = $3339

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 × 3339}/_{5300 × 9}

= ³³³⁹⁰⁰/₄₇₇₀₀

= 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) = $5300

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3339 (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 $5300

= ⁹/₁₀₀ × 5300

= ^{9 × 5300}/₁₀₀

= ⁴⁷⁷⁰⁰/₁₀₀ = 477

Thus, simple Interest for 1 year = $477

Now,

∵ If the simple Interest is $477, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₇ years

∴ If the simple Interest is $3339, then the time = ¹/₄₇₇ × 3339 years

= ^{1 × 3339}/₄₇₇ years

= ³³³⁹/₄₇₇ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(6) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

(8) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.