Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6600

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $11352

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 = $11352 – $6600 = $4752

Thus, Simple Interest = $4752

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 × 4752}/_{6600 × 9}

= ⁴⁷⁵²⁰⁰/₅₉₄₀₀

= 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) = $6600

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4752 (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 = 9% of Principal

= 9% of $6600

= ⁹/₁₀₀ × 6600

= ^{9 × 6600}/₁₀₀

= ⁵⁹⁴⁰⁰/₁₀₀ = 594

Thus, simple Interest for 1 year = $594

Now,

∵ If the simple Interest is $594, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₉₄ years

∴ If the simple Interest is $4752, then the time = ¹/₅₉₄ × 4752 years

= ^{1 × 4752}/₅₉₄ years

= ⁴⁷⁵²/₅₉₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(4) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?

(7) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.