Question

5. You deposit P1000 into a 9% account today. At the end of two years, you will deposit another P3,000. In five years, you plan a P4000 purchase. How much is left in the account one year after the purchase?

Answer 1

Answer:

Step-by-step explanation:

Since we are talking about compounded annual interest, we can use the Exponential Growth Formula to calculate the answer for this question.

$y = a* (1+r)^{t}$

Where:

1. y is the total amount after a given time
2. a is the initial amount
3. r is the interest rate in decimal form
4. t is the amount of time

First we need to calculate the total after 2 years with a 9% interest.

$y = 1000* (1+0.09)^{2}$

$y =  1000* (1.09)^{2}$

$y = 1000* 1.1881$

$y = 1188.1$

So after 2 years there will be £1,188.10 in the account. Now we can add £3000 to that and use the new value as the initial amount, and calculate the new total in 5 years.

$y = (1188.1+3000)* (1+0.09)^{5}$

$y = 4188.1* (1.09)^{5}$

$y = 4188.1* 1.5386$

$y = 6443.91$

So now we can subtract the £4000 purchase from the amount currently in the account, and calculate one more year of interest with the new initial amount.

$y = (6443.91-4000)* (1+0.09)^{1}$

$y = (2443.91)* 1.09$

$y = 2663.86$

So at the end you would have £2,662.86 in the account one year after the purchase.