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 $9593 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) = 9% per annum

Amount (A) = $9593

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 = $9593 – $5300 = $4293

Thus, Simple Interest = $4293

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 × 4293}/_{5300 × 9}

= ⁴²⁹³⁰⁰/₄₇₇₀₀

= 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) = 9% per annum

Simple Interest = $4293 (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 $4293, then the time = ¹/₄₇₇ × 4293 years

= ^{1 × 4293}/₄₇₇ years

= ⁴²⁹³/₄₇₇ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.

(3) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(5) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.

(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

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