Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $9291

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 = $9291 – $5700 = $3591

Thus, Simple Interest = $3591

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 × 3591}/_{5700 × 7}

= ³⁵⁹¹⁰⁰/₃₉₉₀₀

= 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) = $5700

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

Simple Interest = $3591 (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 $5700

= ⁷/₁₀₀ × 5700

= ^{7 × 5700}/₁₀₀

= ³⁹⁹⁰⁰/₁₀₀ = 399

Thus, simple Interest for 1 year = $399

Now,

∵ If the simple Interest is $399, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₉ years

∴ If the simple Interest is $3591, then the time = ¹/₃₉₉ × 3591 years

= ^{1 × 3591}/₃₉₉ years

= ³⁵⁹¹/₃₉₉ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.

(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.

(8) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?