Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $10318

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 = $10318 – $6700 = $3618

Thus, Simple Interest = $3618

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 × 3618}/_{6700 × 6}

= ³⁶¹⁸⁰⁰/₄₀₂₀₀

= 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) = $6700

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3618 (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 = 6% of Principal

= 6% of $6700

= ⁶/₁₀₀ × 6700

= ^{6 × 6700}/₁₀₀

= ⁴⁰²⁰⁰/₁₀₀ = 402

Thus, simple Interest for 1 year = $402

Now,

∵ If the simple Interest is $402, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₂ years

∴ If the simple Interest is $3618, then the time = ¹/₄₀₂ × 3618 years

= ^{1 × 3618}/₄₀₂ years

= ³⁶¹⁸/₄₀₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.

(2) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(5) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(7) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(9) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.