Question 165322
Your tutor must have taken the weekend off!
We'll use the formula for simple interest in this problem:
{{{A = P(1+ni)}}} Where A = the amount you will have after n years of P dollars invested at an interest rate of i per year (simple interest...not compounded).
Let's calculate the two amounts that you will have ({{{A[1]}}}) and ({{{A[2]}}}) from the two principal amounts invested ({{{P[1] = 10000}}} for 2 years and {{{P[2] = 3500}}} for 1 year). You are told that the sum of these two equals $15,569.75
{{{A[1] = P[1](1+ni)}}} Substitute: {{{P[1] = 10000}}} and {{{n = 2}}}
{{{A[1] = 10000(1+2i)}}} The amount at the end of 2 years from the $10,000.
{{{A[2] = P[2](1+ni)}}} Substitute: {{{P[2] = 3500}}} and {{{n = 1}}}
{{{A[2] = 3500(1+i)}}} The amount at the end of 2 years from the $3,500.
{{{A[1]+A[2] = 15569.75}}} The total amount at the end of two years. Substituting the {{{A[1]}}} and {{{A[2]}}} we get:
{{{10000(1+2i)+3500(1+i) = 15569.75}}} Simplify.
{{{10000+20000i + 3500+3500i = 15569.75}}} Combine like-terms.
{{{13500+23500i = 15569.75}}} Subtract 13500 from both sides.
{{{23500i = 2069.75}}} Divide both sides by 23500.
{{{i = 0.08807}}} Multiply by 100 to get the percent interest rate.
i = 8.807%
The interest rate is 8.807%
Check:
{{{A[1] = 10000(1+2(0.08807))}}}
{{{A[1] = 10000(1.17614)}}}
{{{A[1] = 11761.4}}}
{{{A[2] = 3500(1+0.08807)}}}
{{{A[2] = 3500(1.08807)}}}
{{{A[2] = 3808.245}}}
{{{A[1]+A[2] = 11761.42+3808.245}}}
{{{A[1]+A[2] = 15569.665}}} Not quite equal to $15569.75 but very close!