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) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.