+16 scott borrowed $3500 to cover the costs of taking a firefighter course in texas . his bank offered him a simple interest loan at a rate of 4.7% with single repayment in 6 months. another bank offered him a loan that was compounded monthly at an annual rate of 4.2% with a single repayment in 6 months . which option would cost him the least amount of interest and by how much less ?
scott borrowed $3500 to cover the costs of taking a firefighter course in texas . his bank offered him a simple interest loan at a rate of 4.7% with single repayment in 6 months. another bank offered him a loan that was compounded monthly at an annual rate of 4.2% with a single repayment in 6 months . which option would cost him the least amount of interest and by how much less ?
Option @ 4.7% = 3,500 x 4.7% =$164.50 simple annual interest.
$164.50 / 2 =$82.25 this is what Scott will pay in 6 months at simple interest.
Option@ 4.2% =3,500 x (1 +0.042/12)^6 =3,500 x 1.0035^6=$3,574.15.
$3,574.15 - $3,500 =$74.15 this is what Scott will pay in 6 months at compounded interest.
The compound option is cheaper by: $82.25 - $74.15 =$8.10.
