Question

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

compounded quarterly, for how long should you deposit the money in order
have $9600? how many years

Answer 1

18 years

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 + (r)/(n))^(nt)`

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

We can rearrange the above equation to:

`(A)/(P) = (1 + (r)/(n))^(nt)`

Taking logs on both sides

`log((A)/(P)) = log(1 + (r)/(n))^(nt)`

This gives

`log((A)/(P)) =nt * log(1 + (r)/(n))\\So,\\nt = (log((A)/(P)))/( log(1 + (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