Question

Olivia deposited $2,136.70 into a saving account with an interest rate of 2.7% compounded quarterly. About how long will it take for the account to be worth $4,000?

Answer 1

Answer:

23.26 years

Step-by-step explanation:

Use the compound interest formula:

A = P $( 1 + \frac{r}{100n} )^{nt}$

A =  final amount

P =  initial principal balance

r =  interest rate

n =  number of times interest applied per time period

t =  number of time periods elapsed

P = $2,136.70

r = 2.7

n = 4

A = $4,000

Now we plug everything in and solve for t.

$4,000 = $2,136.70 $(1 + \frac{2.7}{100 * 4} )^{4t}$

$4,000 = $2,136.70 $(1 + .00675 ) ^{4t}$

$4,000 = $2,136.70$(1.00675)^{4t}$ Divide each side by $2,136.70

$4,000/$2,136.70 = $(1.00675)^{4t}$

1.87 = $(1.00675)^{4t}$

log (1.87) = log $(1.00675)^{4t}$

log 1.87 = (4t) (log 1.00675)  Divide each side by (log 1.00675)

$\frac{log 1.87}{log 1.00675}$ = 4t

93.044 = 4t Divide each side by 4.

93.044/4 = t

23.26 = t

23.26 years

Answer 2

Answer:

23.3 years

Step-by-step explanation:

4000 = 2136.7(1 + .027/4)^(4t)

4000 / 2136.7 = 1.00675^4t

ln (4000 / 2136.7) / ln 1.00675^4 = t

23.301690290541729158877031400229 = t

23.3 years