Question

A $10,000 deposit at the bank will double in value in 9 years. Give a formula for the accumulated amount t years after the investment is made

Answer 1

Answer:

$S = P(1.08)^{t}$

Step-by-step explanation:

A $10,000 deposit at the bank will double in value in 9 years.

If the interest is r% and it is compounded each year, then we can write from the formula of compound interest that

$20000 = 10000(1 + \frac{r}{100})^{9}$

⇒ $2 = (1 + \frac{r}{100})^{9}$

⇒ $1 + \frac{r}{100} = 1.08$

⇒ r = 8%

Therefore, the formula for the accumulated amount t years after the investment is made will be  

$S = P(1 + \frac{8}{100})^{t} = P(1.08)^{t}$  

where, P is the invested principal and S is the accumulated sum. (Answer)