Alan invests a total of ​$16,500 in three different ways. He invests one part in a mutual fund which in the first year has a return of​ 11%. He invests the second part in a government bond at​ 7% per year. The third part he puts in the bank at​ 5% per year. He invests twice as much in the mutual fund as in the bank. The first year​ Alan's investments bring a total return of ​$1,425. How much did he invest in each​ way?

>> $9000 invested in mutual fund

>> $3000 invested in government bond

>> $4500 put in the bank

Step-by-step explanation:

Let us denote the money invested in each case by a letter. Thus;

a = the money that he invested in a mutual fund

b = the money that he invested in a government bond

c = the money that he put in the bank

We are told that he invested a total of ​$16,500. Thus;

a + b + c = 16500 - - - (eq 1)

He invested twice as much in the mutual fund as he did in the bank. Thus;

a = 2c - - - (eq 2)

From the percentage given and the return of ​$1,425 from the first year investments, we have;

0.11a + 0.07b + 0.05c = 1425 - - - (eq 3)

Let's put 2c for a in eq (1) and eq (3)

Thus;

2c + b + c = 16500

b + 3c = 16500 - - - (eq 4)

Also,

0.11(2c) + 0.07b + 0.05c = 1425

0.07b + 0.27c = 1425 - - - (eq 5)

From eq 4, b = 16500 - 3c

Putting this in eq(5) gives;

0.07(16500 - 3c) + 0.27c = 1425

1155 - 0.21c + 0.27c = 1425

0.06c = 1425 - 1155

0.06c = 270

c = 270/0.06

c = $4500

b = 16500 - 3(4500)

b = 16500 - 13500

b = $3000

Since a = 2c, then;

a = 2(4500)

a = $9000

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation:

2

step-by-step explanation: