Question

Sally invested R10000 into a savings account. The interest rate for the first two years was 8% p.a. compounded monthly. Thereafter, it changed to 11,5% p.a. compounded semi-annually. After the first year she also deposited an additional R500 into the account and another R1000 after 5 years. How much did she have in her account after 6 years? ​

Answer 1

To calculate how much Sally had in her account after 6 years, we'll break down the calculations into different periods and compounding frequencies:

1. For the first 2 years at 8% p.a. compounded monthly:
- Principal (P1) = R10,000
- Annual Interest Rate (r1) = 8% or 0.08
- Compounding Frequency (n1) = 12 times a year
- Time (t1) = 2 years

Using the formula for compound interest:

A1 = P1 * (1 + r1/n1)^(n1*t1)

A1 = 10,000 * (1 + 0.08/12)^(12*2)

2. After the first year, she deposited an additional R500. So, for the second year at 8% with monthly compounding:

- Principal (P2) = A1 (the amount calculated above)
- Annual Interest Rate (r1) = 8% or 0.08
- Compounding Frequency (n1) = 12 times a year
- Time (t1) = 1 year

A2 = (P2 + 500) * (1 + 0.08/12)^(12*1)

3. At the end of the second year, Sally deposits an additional R1,000. After that, the interest rate changes to 11.5% p.a. compounded semi-annually.

- Principal (P3) = A2 (the amount calculated above)
- Annual Interest Rate (r2) = 11.5% or 0.115
- Compounding Frequency (n2) = 2 times a year
- Time (t2) = 4 years (total time remaining is 6 years - 2 years already accounted for)

A3 = (P3 + 1000) * (1 + 0.115/2)^(2*4)

Now, calculate A3 to find out how much Sally had in her account after 6 years. A3 will represent the total amount in her account after all the deposits and interest calculations.

A3 = (A2 + 1000) * (1 + 0.115/2)^(2*4)

Calculate A3 to find the final amount.