Question

Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has $3,875.79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account?
Compound interest formula:mc007-1.jpg

t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years


2 years
9 years
18 years
36 years

Answer 1

T=(log(3,875.79÷1,900)÷log(1+0.02))÷2
T=18 years

Answer 2

Answer:

Option 3 is correct. After 18 years the amount will $3,875.79.

Step-by-step explanation:

The compound interest formula is

$v(t)=p(1+\frac{r}{n})^{nt}$

Where, t = years since initial deposit

n = number of times compounded per year

r = annual interest rate (as a decimal)

P = initial (principal) investment

V(t) = value of investment after t years.

The initial amount is $1,900. Interest rate is 4% and interest compounded semiannually. It means interest compounded 2 times in a year. The amount after t years is  $3,875.79.

$3,875.79=1900(1+\frac{0.04}{2})^{2t}$

$3,875.79=1900(1.02)^{2t}$

$\frac{3,875.79}{1900}=(1.02)^{2t}$

$log(\frac{3,875.79}{1900})=log(1.02)^{2t}$

$\frac{0.309606636902}{log(1.02)}=2t$

$t=18$

After 18 years the amount will $3,875.79.

Therefore the option 3 is correct.