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 $6120 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $6120

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 = $6120 – $4500 = $1620

Thus, Simple Interest = $1620

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 × 1620}/_{4500 × 6}

= ¹⁶²⁰⁰⁰/₂₇₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $1620 (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 $1620, then the time = ¹/₂₇₀ × 1620 years

= ^{1 × 1620}/₂₇₀ years

= ¹⁶²⁰/₂₇₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(5) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.

(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?