Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $7546

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 = $7546 – $4900 = $2646

Thus, Simple Interest = $2646

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 × 2646}/_{4900 × 6}

= ²⁶⁴⁶⁰⁰/₂₉₄₀₀

= 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) = $4900

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

Simple Interest = $2646 (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 $4900

= ⁶/₁₀₀ × 4900

= ^{6 × 4900}/₁₀₀

= ²⁹⁴⁰⁰/₁₀₀ = 294

Thus, simple Interest for 1 year = $294

Now,

∵ If the simple Interest is $294, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₉₄ years

∴ If the simple Interest is $2646, then the time = ¹/₂₉₄ × 2646 years

= ^{1 × 2646}/₂₉₄ years

= ²⁶⁴⁶/₂₉₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(3) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(7) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?

(9) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.