Solution:
Given that,
Antonio wants to invest $7600 in a saving account
Antonio’s investment to double in value in 12 years
To find: Rate of interest
The total amount using simple interest is given as:
[tex]A = p(1+\frac{r}{100}t)[/tex]
Where,
p is the principal
r is the rate of interest
t is the number of years
From given,
p = 7600
t = 12 years
r = ?
Antonio’s investment to double
Therefore,
A = 2(7600) = 15200
Substituting the values we get,
[tex]15200 = 7600(1 + \frac{r}{100} \times 12)\\\\\frac{15200}{7600} = 1 + 0.12r\\\\2 = 1 + 0.12r\\\\0.12r = 2 - 1\\\\0.12r = 1\\\\r = 8.333 \%[/tex]
[tex]r \approx 8.3 \%[/tex]
Thus interest rate required for Antonio’s investment to double in value in 12 years is 8.3 % per annum