Alyssa received $30,000 from an inheritance and invests part in a certificate of deposit (CD) paying 5% annual interest and the rest in Apple Inc. offering an annual return of 11%. If the annual income from her investments is $2,220, how much did Alyssa invest in each?

Question

Mathematics

Karma Carroll

9 August, 14:14

Alyssa received $30,000 from an inheritance and invests part in a certificate of deposit (CD) paying 5% annual interest and the rest in Apple Inc. offering an annual return of 11%. If the annual income from her investments is $2,220, how much did Alyssa invest in each?

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Makenna · Answer 1

The annual income (A) is equal to the difference of future worth (F) and the present worth (P). Since the formula of F is:

F = P (1+i) ⁿ, then,

A = F - P

A = P[ (1+i) ⁿ - 1] = $2,220, where n=1 because annual means income per one year

Now, amount of P should be distributed such that the total would be $30,000. Thus, the equation should be

(30,000 - x) [1 + 0.05 - 1] + x[1 + 0.11 - 1) = 2220

Solving for x,

x = 12,000

30,000 - x = 18,000

Hence, Alyssa placed $12,000 in the certificate of deposit, and $18,000 with Apple Inc.