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

`S = P(1.08)^(t)`

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 + (r)/(100))^(9)`

⇒
`2 = (1 + (r)/(100))^(9)`

⇒
`1 + (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 + (8)/(100))^(t) = P(1.08)^(t)`

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