Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $9916

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 = $9916 – $6700 = $3216

Thus, Simple Interest = $3216

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 × 3216}/_{6700 × 6}

= ³²¹⁶⁰⁰/₄₀₂₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6700

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

Simple Interest = $3216 (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 $6700

= ⁶/₁₀₀ × 6700

= ^{6 × 6700}/₁₀₀

= ⁴⁰²⁰⁰/₁₀₀ = 402

Thus, simple Interest for 1 year = $402

Now,

∵ If the simple Interest is $402, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₂ years

∴ If the simple Interest is $3216, then the time = ¹/₄₀₂ × 3216 years

= ^{1 × 3216}/₄₀₂ years

= ³²¹⁶/₄₀₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) 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.

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(5) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.

(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.