  # Interest Earned in three different accounts

An affluent investor deposits \$2,000,000 in three different accounts:

a. short term notes paying 4.6% per year
b. three times as much in government bonds paying 4%
c. the balance of the \$2,000,000 in corporate bonds paying 3%.

The total interest income for the year is \$73,000.

How much money was placed in each account?

### Comments for Interest Earned in three different accounts

 Jul 22, 2012 Interest Earned in three different accounts by: Staff The answer: Total Interest Earned = interest from short term notes + interest from government bonds + interest from corporate bonds N = dollar amount invested in short term notes G = dollar amount invested in government bonds C = dollar amount invested in corporate bonds a. short term notes paying 4.6% per year interest from short term notes = N*.046 b. government bonds paying 4% interest from government bonds = G*.04 c. corporate bonds paying 3%. interest from corporate bonds = C*.03 Total Interest Earned = N*.046 + G*.04 + C*.03 There is three times as much invested in government bonds than invested in short term notes G = 3N Substituting 3N for G in the equation for Total Interest Earned Total Interest Earned = N*.046 + G*.04 + C*.03 Total Interest Earned = N*.046 + 3N *.04 + C*.03 The balance of the \$2,000,000 is invested in corporate bonds C = \$2,000,000 - (short term notes + government bonds) C = \$2,000,000 - (N + G) C = \$2,000,000 - (N + 3N) Substituting \$2,000,000 - (N + 3N) for C in the equation for Total Interest Earned Total Interest Earned = N*.046 + 3N *.04 + C*.03 Total Interest Earned = N*.046 + 3N *.04 + (\$2,000,000 - (N + 3N))*.03 Total Interest Earned = \$73,000 \$73,000 = N*.046 + 3N *.04 + (\$2,000,000 - (N + 3N))*.03 Solve for N 73000 = N*.046 + 3N *.04 + (2000000 - (N + 3N))*.03 73000 = N*.046 + 3N *.04 + (2000000 - 4N)*.03 73000 = .046N + 0.12N + (2000000 - 4N)*.03 73000 = 0.166N + (2000000 - 4N)*.03 73000 = 0.166N + (2000000 - 4N)*.03 73000 = 0.166N + (2000000*.03) - (4N)*.03 73000 = 0.166N + 60000 - .12N 73000 = 0.166N - .12N + 60000 73000 = 0.046N + 60000 73000 - 60000 = 0.046N + 60000 - 60000 13000 = 0.046N + 0 13000 = 0.046N 0.046N = 13000 0.046N / 0.046 = 13000 / 0.046 N * (0.046 / 0.046) = 13000 / 0.046 N * (1) = 13000 / 0.046 N = 13000 / 0.046 N = 282608.69565217389 N = 282608.70 N = \$282,608.70 Compute G G = 3N G = 3*282608.70 G = 847826.09999999998 G = 847826.10 G = \$847,826.10 Compute C C = \$2,000,000 - (short term notes + government bonds) C = \$2,000,000 - (N + G) C = \$2,000,000 - (\$282,608.70 + \$847,826.10) C = 2000000 - (1130434.80) C = 2000000 - 1130434.80 C = 869565.20 C = \$869,565.20 >>> the final answer is: N = dollar amount invested in short term notes = \$282,608.70 G = dollar amount invested in government bonds = \$847,826.10 C = dollar amount invested in corporate bonds = \$869,565.20 ----------------------------------------------------------------- Check the answers: Total Interest Earned = N*.046 + G*.04 + C*.03 73000 = 282608.70 *.046 + 847826.10 * .04 + 869565.20 * .03 73000 = 13000.00 + 33913.04 + 26086.96 73000 = 73000, OK → N, G, and C are valid solutions Thanks for writing. Staff www.solving-math-problems.com