Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $13400

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 = $13400 – $6700 = $6700

Thus, Simple Interest = $6700

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 × 6700}/_{6700 × 10}

= ⁶⁷⁰⁰⁰⁰/₆₇₀₀₀

= 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) = $6700

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

Simple Interest = $6700 (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 $6700

= ¹⁰/₁₀₀ × 6700

= ^{10 × 6700}/₁₀₀

= ⁶⁷⁰⁰⁰/₁₀₀ = 670

Thus, simple Interest for 1 year = $670

Now,

∵ If the simple Interest is $670, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₇₀ years

∴ If the simple Interest is $6700, then the time = ¹/₆₇₀ × 6700 years

= ^{1 × 6700}/₆₇₀ years

= ⁶⁷⁰⁰/₆₇₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.

(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(5) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.