Answer to Question #302676 in Financial Math for Fancy

Question

Andile deposits R900 into a savings account paying 6,5% interest per year, compounded quarterly. After three and a half years he withdraws R1000 from the account and deposits it into a second account paying 11% simple interest per year. How much is the total amount accrued in the first account two years after withdrawing the R1000?

Answer 1

Compound interest formula:

P{1+r/k}^nk

Where p is the initial investment

R is the rate of interest

N is the period of investment

K is the number of times that interest was applied per time period

Since interest is compounded quarterly, the rate of interest is 6.5%/4=0.01625 and the period of investment will be 3.5*4=14

Replacing the above figures in the equation we get:

900(1+0.01625)¹⁴=1127.85

So after three and a half years, the total accumulated amount will be 1127.85

After withdrawal the remaining amount in the first account will be (1127.85-1000)=127.85

In two years, this balance will have accumulated to 145.45 as shown below:

127.85(1.01625)⁸

=R145.45

Therefore, R145.45 is the total amount that will have accrued in the first account two years after withdrawing the R1000