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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?



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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





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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



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