Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9200

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 = $9200 – $4600 = $4600

Thus, Simple Interest = $4600

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 × 4600}/_{4600 × 10}

= ⁴⁶⁰⁰⁰⁰/₄₆₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 10% per annum

Simple Interest = $4600 (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 = 10% of Principal

= 10% of $4600

= ¹⁰/₁₀₀ × 4600

= ^{10 × 4600}/₁₀₀

= ⁴⁶⁰⁰⁰/₁₀₀ = 460

Thus, simple Interest for 1 year = $460

Now,

∵ If the simple Interest is $460, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₀ years

∴ If the simple Interest is $4600, then the time = ¹/₄₆₀ × 4600 years

= ^{1 × 4600}/₄₆₀ years

= ⁴⁶⁰⁰/₄₆₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?

(7) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.

(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.