Question

You have $5600. The best interest rate you can find is 3%

Answer 1

Answer:

18 years

Step-by-step explanation:

The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by

$A = P(1 + \frac{r}{n})^{nt}$

Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03

We can rearrange the above equation to:

$\frac{A}{P} = (1 + \frac{r}{n})^{nt}$

Taking logs on both sides

$log(\frac{A}{P}) = log(1 + \frac{r}{n})^{nt}$

This gives

$log(\frac{A}{P}) =nt \times log(1 + \frac{r}{n})\\So,\\nt = \frac{log(\frac{A}{P})}{ log(1 + \frac{r}{n})}$

In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075

1 + r/n = 1+0.0075 = 1.0075

4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72

t = 72/4 = 18 years