Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7844

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 = $7844 – $5300 = $2544

Thus, Simple Interest = $2544

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 × 2544}/_{5300 × 6}

= ²⁵⁴⁴⁰⁰/₃₁₈₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 6% per annum

Simple Interest = $2544 (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 = 6% of Principal

= 6% of $5300

= ⁶/₁₀₀ × 5300

= ^{6 × 5300}/₁₀₀

= ³¹⁸⁰⁰/₁₀₀ = 318

Thus, simple Interest for 1 year = $318

Now,

∵ If the simple Interest is $318, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₈ years

∴ If the simple Interest is $2544, then the time = ¹/₃₁₈ × 2544 years

= ^{1 × 2544}/₃₁₈ years

= ²⁵⁴⁴/₃₁₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.

(4) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(5) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.

(7) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?

(9) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(10) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.