At the beginning of every year, a man deposited $ 10,000 in a financial institution which paid compound interest at the rate of 20% p.a. He stopped further deposits after three years. The Money remained invested in the financial institution for a further eight years.
(a) How much money did he have at the end of the first three years? (4 marks)
Amount =p (1+ r)^n
= 10000(1+.2)^3
=17,280
(b) How much interest did the money generate in the entire period?
Amount – interest
Amount = p (1 + r)^n
=10000(1.2)^8– 10000
= 429998.17 – 10000
=32998.17
To find the amount of money the man had at the end of the first three years, we need to use the compound interest formula. The formula states:
Amount = Principal * (1 + interest rate)^time
In this case, the Principal is $10,000, the interest rate is 20% (or 0.2), and the time is 3 years. Plugging these values into the formula, we get:
Amount = $10,000 * (1 + 0.2)^3
= $10,000 * 1.2^3
= $10,000 * 1.728
= $17,280
Therefore, the man had $17,280 at the end of the first three years.
To calculate the interest generated in the entire period, we subtract the principal amount from the total amount at the end of the period.
Interest = Amount - Principal
Using the same formula, we can find the total amount at the end of the period. In this case, the time is 8 years (3 initial years + 8 additional years), and the principal is still $10,000. Plugging in these values, we get:
Amount = $10,000 * (1 + 0.2)^8
= $10,000 * 1.2^8
= $10,000 * 4.2999817
= $42,999.81
Now, we can calculate the interest:
Interest = $42,999.81 - $10,000
= $32,999.81
Therefore, the money generated $32,999.81 in interest during the entire period.