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) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?

(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?

(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.

(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?

(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.