Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6109

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 = $6109 – $4100 = $2009

Thus, Simple Interest = $2009

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 × 2009}/_{4100 × 7}

= ²⁰⁰⁹⁰⁰/₂₈₇₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4100

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2009 (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 = 7% of Principal

= 7% of $4100

= ⁷/₁₀₀ × 4100

= ^{7 × 4100}/₁₀₀

= ²⁸⁷⁰⁰/₁₀₀ = 287

Thus, simple Interest for 1 year = $287

Now,

∵ If the simple Interest is $287, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₇ years

∴ If the simple Interest is $2009, then the time = ¹/₂₈₇ × 2009 years

= ^{1 × 2009}/₂₈₇ years

= ²⁰⁰⁹/₂₈₇ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

(3) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.

(6) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(9) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.