Question

6) Alberto invests $8,534 in a retirement

Answer 1

Answer:

It will take 17.2 years to reach account balance of $16826.03

Step-by-step explanation:

Given

Principal amount P = $ 8534

rate of interest r = 4% = 4/100 = 0.04

No of times interest is compounded, n = 12

Final amount A = $ 16826.03

To find: time in years, t = ?

We know that final amount of compound interest A is given by formula:

A = P $(1 + \frac{r}{n} )^{nt}$

Substituting known values,

16826.03 = 8534 * $(1 + \frac{0.04}{12} )^{12t}$

$(1 + \frac{0.04}{12} )^{12t}$ = 1.972

$(1.0033)^{12t}$ = 1.972

take log on both sides,

ln $(1.0033)^{12t}$ = ln (1.972)

12t * ln (1.0033) = ln (1.972)     (since ln $x^{n}$ = n * ln x)

12t = 206.112

t = 17.2 years

Answer 2

Answer:

  17 years

Step-by-step explanation:

The compound interest formula is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r, compounded n times per year for t years.

Filling in the numbers and solving for t, we find ...

  16826.03 = 8534(1 +.04/12)^(12t)

  16826.03/8534 = 1.0033333...^(12t)

Taking logs, we have ...

  log(16826.03/8534) = 12t·log(1.0333333...)

Dividing by the coefficient of t gives ...

  log(16826.03/8534)/(12·log(301/300)) = t ≈ 17.000

It will take 17 years for the account balance to reach $16,826.03.