Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $6930

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 = $6930 – $4500 = $2430

Thus, Simple Interest = $2430

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 × 2430}/_{4500 × 6}

= ²⁴³⁰⁰⁰/₂₇₀₀₀

= 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) = $4500

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

Simple Interest = $2430 (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 $4500

= ⁶/₁₀₀ × 4500

= ^{6 × 4500}/₁₀₀

= ²⁷⁰⁰⁰/₁₀₀ = 270

Thus, simple Interest for 1 year = $270

Now,

∵ If the simple Interest is $270, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₇₀ years

∴ If the simple Interest is $2430, then the time = ¹/₂₇₀ × 2430 years

= ^{1 × 2430}/₂₇₀ years

= ²⁴³⁰/₂₇₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(4) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(6) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.