Question

Antonio wants to invest $7600 in a saving account. Determine the interest rate (simple interest) required for Antonio’s investment to double in value in 12 years.

Answer 1

Interest rate required for Antonio’s investment to double in value in 12 years is 8.3 % per annum

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:

$A = p(1+\frac{r}{100}t)$

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,

$15200 = 7600(1 + \frac{r}{100} \times 12)\\\\\frac{15200}{7600} = 1 + 0.12r\\\\2 = 1 + 0.12r\\\\0.12r = 2 - 1\\\\0.12r = 1\\\\r = 8.333 \%$

$r \approx 8.3 \%$

Thus interest rate required for Antonio’s investment to double in value in 12 years is 8.3 % per annum