Question

what annual interest rate is required for a debt of $10406 to grow into $13038 in 6 years if interest compounds monthly?

Answer 1

Let required annual interest rate be x %.

The formula for future value (F) of an initial value (P), after n years, where interest rate is r % and interest is compounded t times per year is F = P(1+r/100t)^nt .

Here, P = $ 10406, F = $ 13038 , t= 12 and n = 6. Therefore, 13038 = 10406( 1+x/1200)^6*12 or, (1+x/1200)⁷² = 13038/10406 = 1.2529301 so that (1+x/1200) = (1.2529301 )^1/72 = 1.003136654. Hence x/1200 = 1.003136654 -1 = .003136654 so that x = 0.003136654 *1200 =3.7639848 say 3.764 ( on rounding off to 3 decimal places).

Thus, an annual interest rate of 3.764 % is required for a debt of $10406 to grow into $13038 in 6 years if interest compounds monthly