Question

John deposits R900,00 into a savings account paying 6,5% interest per year, compounded
quarterly. After three and a half years he withdraws R1 000,00 from the account. How much
is the total amount accrued in the account two years after withdrawing the R1 000,00? The
correct answer, rounded to the nearest rand, is [1] R128,00. [2] R145,00. [3] R283,00. [4] R1 138,00.

Answer 1

Given :

The principal deposited in account = p = Rs 90000

The rate of interest = r = 6.5% compounded quarterly

The time period = 3.5 years

After 3.5 years, amount withdrawal = Rs 100000

To Find :

The total amount accrued in the account two years after withdrawing Rs 100000

Solution :

From Compound Interest

Amount = Principal × $(1+\dfrac{rate}{4\times 100})^{4\times time}$

Or,   A = Rs 90000 × $(1+\dfrac{6.5}{4\times 100})^{4\times 3.5}$

Or,   A = Rs 90000 × 1.253

∴  Amount = A = Rs 112770

Since, Rs 100000 withdraw from account

So,  Amount left in account = Rs 112770 - Rs 100000

                                             = Rs 12770

Again

For the next two years, at same rate of interest

Amount = Principal × $(1+\dfrac{rate}{4\times 100})^{4\times time}$

Or,   A = Rs 12770 × $(1+\dfrac{6.5}{4\times 100})^{4\times 2}$

Or,   A = Rs 12770 × 1.137

∴  Amount = A = Rs 14527.6

Hence, The total amount accrued in the account two years after withdrawing Rs 100000 is Rs 14528           Answer