Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $7084

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 = $7084 – $4600 = $2484

Thus, Simple Interest = $2484

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 × 2484}/_{4600 × 9}

= ²⁴⁸⁴⁰⁰/₄₁₄₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4600

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

Simple Interest = $2484 (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 $4600

= ⁹/₁₀₀ × 4600

= ^{9 × 4600}/₁₀₀

= ⁴¹⁴⁰⁰/₁₀₀ = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₄ years

∴ If the simple Interest is $2484, then the time = ¹/₄₁₄ × 2484 years

= ^{1 × 2484}/₄₁₄ years

= ²⁴⁸⁴/₄₁₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?

(2) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.

(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?

(7) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.

(10) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.