Novia is investing $2517 in an account compounded monthly. She wants to have $3000 in 3 years for a trip to Europe.
What interestrate,to the nearest hundredth of a percent, compounded monthly, does she need?
Novia's initial investment is $2517 in an account where the interest is compounded monthly.
Her target amount at the end of 3 years is $3000. Let the required interest rate be R% annually. As the interest is compounded monthly, the formula of the amount at the end of 3 years is 2517*(1+r)^t, where t = 12*3 = 36 months and the rate r is R/12.
This gives 3000 = 2517*(1+r)^36
=> (1+r)^36 = 3000/2517
Take the log of both the sides
=> 36*log(1+r) = log(3000/2517)
=> log(1+r) = 2.1177*10^-3
=> 1+r = 10^(2.1177*10^-3)
=> 1+r = 1.00488
=> r = 0.00488
The monthly rate of interest required is 0.49%
=> R = 5.87%
The required annual rate of interest is 5.87%