Question

if the debt of a loan increases by 27% in 6 years, what is the loan's equivalent annual rate

Answer 1

Let the loan amount be $ L and let the loan's equivalent annual rate be x %.

Assuming a simple rate of interest, L * (x/100)* 6 = 0.27L or, 3Lx/50 = 0.27L . On dividing both the sides by L, we get 3x/50 = 0.27 so that x = (0.27)*50/3 = 4.50

Assuming annual compounding of interest, L *(1+x/100)⁶ = 1.27L . On dividing both the sides by L, we get (1+x/100)⁶ = 1.27 so that 1+x/100 = (1.27)^1/6 = 1.04064025. Then x/100 = 0.04064025 so that x = 4.064 .

Hence, in case of simple interest, the loan's equivalent annual rate is 4.5 % and in case of annual compounding of interest, the loan's equivalent annual rate is 4.064 % ( on rounding off to 3 decimal places).