Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $10452

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 = $10452 – $6700 = $3752

Thus, Simple Interest = $3752

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 × 3752}/_{6700 × 7}

= ³⁷⁵²⁰⁰/₄₆₉₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 7% per annum

Simple Interest = $3752 (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 $6700

= ⁷/₁₀₀ × 6700

= ^{7 × 6700}/₁₀₀

= ⁴⁶⁹⁰⁰/₁₀₀ = 469

Thus, simple Interest for 1 year = $469

Now,

∵ If the simple Interest is $469, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₉ years

∴ If the simple Interest is $3752, then the time = ¹/₄₆₉ × 3752 years

= ^{1 × 3752}/₄₆₉ years

= ³⁷⁵²/₄₆₉ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?

(5) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?

(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(8) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?