Question

Kayla currently has an account balance of $2,134.96. She opened the account 12 years ago with a deposit of $1,327.35. If the interest compounds twice a month, what is the interest rate on the account?

Answer 1

u have P0=1327.35 as your initial deposit.

if r is the interest rate, then one term after you would have
\[\large P_1=P_0+rP_0=(1+r)P_0 \]
for the second term
\[\large P_2=P_1+rP_1=(1+r)P_1=(1+r)(1+r)P_0=(1+r)^2P_0 \]
then after k terms you would have
\[\large P_k=(1+r)^kP_0 \]

Answer 2

u have
\[\large P_0=1327.35\quad\text{and}\quad P_k=2134.96 \]
the question is k=?

and then u solve the equation for r

Answer 3

Here is the compound interest formula: \[\Large A = P(1 + \frac{ r }{ n })^{nt}\]
A = Amount at maturity = $2,134.96
P = Principal Amount = $1,327.35
r = Annual interest rate in decimal = ?
n = compounding period = 2 (because compounded twice a year)
t = years invested = 12
Substitute and solve for r. Convert r from decimal to percentage.

Answer 4

Sorry n = 24 (compounded twice a month).

Answer 5

okay so 2,134.96=1,327.35(1+r/2)^24

Answer 6

2,134.96=1,327.35(1+r/24)^288
Two changes to what you have:
1) changed r/2 to r/24 and
2) the exponent should be 288. n = 24, t = 12, nt = 24*12 = 288

Answer 7

uhhh okay so it would be 2,134.96=1,327.35(1+r/24)^288? I'm not really sure how to get r though

Answer 8

Yeah, initially I thought it was compounded twice a year and said n = 2. But a minute later I corrected that to n = 24 in the subsequent comment.

Answer 9

First divide both sides by 1327.35
Then take the 288th root on both sides. That is raise both sides to ^(1/288)

Answer 10

okay so 1.60843786^(1/288)=?

Answer 11

2,134.96 = 1,327.35 * (1+r/24)^288
2,134.96 / 1,327.35 = (1+r/24)^288
1.60843786 = (1+r/24)^288
1.60843786^(1/288) = (1 + r/24)
Use your calculator or Google calculator to compute the left side.

Answer 12

I got 1.00165158262

Answer 13

1.00165158262 = (1 + r/24)
Subtract 1 from both sides.
Multiply both sides by 24 to get you r

Answer 14

The r will be in decimal. Multiply by 100, round it off to second decimal or so and give your answer in percentage.

Answer 15

i got 0.00688159425 but the only answers are
a. 2.9%
b. 0.3%
c. 4.0%
d. 4.9%

Answer 16

You forgot to multiply both sides by 24 to get r.

Answer 17

oohhhh i divided by accident
i got 3.963798288
so 4.0%?

Answer 18

1.60843786^(1/288) = (1 + r/24)
1.00165158262 = 1 + r/24
subtract 1 from both sides
0.00165158262 = r/24
multiply both sides by 24
0.03963798292 = r
Multiply by 100 to convert to percentage
r = 3.96%
round it off to 4%

Answer 19

okay :D thank you

Answer 20

you are welcome.