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) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(4) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(6) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?