Question

A person plans to invest three times as much in an a.) Artisan International fund at 10% annual interest as in a b.) SEI Large Cap Index fund at 16% annual interest. How much will the person have to invest in each fund to earn a total of $1840 in one year?

Answer 1

We will assume simple interest.

The formula is:

$i=\text{Prt}$

Where

i is the interest amount

P is amount invested (initial amount)

r is rate of interest per year, in decimal

t is time in years

SEI Large Cap Index Fund

He wants to invest certain amount (P) at 16% (16/100=0.16, r = 0.16) for 1 year (t = 1). The interest should be 1840 (for total)

We can write:

$i=P(0.16)(1)$

Artisan Internationl Fund

Invest 3 times as SEi. So, initial = 3P. Interest 10% means 10/100 = 0.1

Time 1 year (t = 1). We can write:

$i=(3P)(0.1)(1)$

Both of these interest expressions sum to an interst of $1840. Thus, we can write:

$1840=0.16P+0.3P$

Now, we can solve for P:

$\begin{gathered} 1840\text{ = 0.46P} \\ P=4000 \\ \text{Thus,} \\ 3P=3\times4000 \\ 3P=12,000 \end{gathered}$

The person has to invest:

$4000 in SEI Large Cap Index, and

$12,000 in Artisan International