If $3800 is invested in a savings account for which interest is compounded quarterly, and if the $3800 turns into $4300 in 2 years, what is the interest rate of the savings account?
let the quarterly rate be i
then 3800(1+i)^8 = 4300
(1+i)^8 = 1.1315789....
take (1/8)th root , (exponent of 1/8)
1+i = 1.01557..
i = .01557...
annual rate is 4i = .06229
the rate is 6.229% per annum, compounded quarterly.
4300=3800(1+i/4)^4t where t is 2, solve for i.
43/38= (1+i/4)^8
take the log of each side
log43-log38=8(1+i/4)
solve for i.
I don't get it
107.80
To find the interest rate of the savings account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, we know:
P = $3800
A = $4300
t = 2 (years)
n = 4 (quarterly compounding)
Now we can rearrange the formula to solve for r:
A/P = (1 + r/n)^(nt)
Substituting the values:
4300/3800 = (1 + r/4)^(4*2)
Now we can solve for r:
1.1316 = (1 + r/4)^8
Taking the 8th root on both sides:
(1 + r/4) = 1.037495
Subtracting 1 from both sides:
r/4 = 0.037495
Multiplying both sides by 4:
r = 0.14998
Therefore, the interest rate of the savings account is approximately 14.998% or 15% (rounded to the nearest percent).