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 $9514 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $9514

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 = $9514 – $6700 = $2814

Thus, Simple Interest = $2814

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 × 2814}/_{6700 × 6}

= ²⁸¹⁴⁰⁰/₄₀₂₀₀

= 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) = $6700

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

Simple Interest = $2814 (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 $2814, then the time = ¹/₄₀₂ × 2814 years

= ^{1 × 2814}/₄₀₂ years

= ²⁸¹⁴/₄₀₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?

(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(3) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?

(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.

(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.