Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7520

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 = $7520 – $4700 = $2820

Thus, Simple Interest = $2820

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 × 2820}/_{4700 × 6}

= ²⁸²⁰⁰⁰/₂₈₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $4700

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

Simple Interest = $2820 (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 $4700

= ⁶/₁₀₀ × 4700

= ^{6 × 4700}/₁₀₀

= ²⁸²⁰⁰/₁₀₀ = 282

Thus, simple Interest for 1 year = $282

Now,

∵ If the simple Interest is $282, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₂ years

∴ If the simple Interest is $2820, then the time = ¹/₂₈₂ × 2820 years

= ^{1 × 2820}/₂₈₂ years

= ²⁸²⁰/₂₈₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

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

(3) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?

(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.