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

Interest rate is 1.728%

Explanation:

Here, we are interested in calculating the monthly interest rate on an account.

Mathematically;

The compound interest formula amount is given as;

A = P( 1 + r/n)^nt

where A is the amount at the end of the compounding = $2,134.96

P is the principal which is the amount deposited = $1,327.35

r is the rate which we want to calculate

n is the number of times per year it is compounded = (2 * 12) = 24 ( twice monthly)

t is the number of years = 12

2,134.96 = 1327.35( 1 + r/24)^(24 * 12)

divide both sides by 1327.35

1.608 = (1 + r/24)^288

Take the ln of both sides

ln 1.608 = ln ( 1 + r/24)^288

ln 1.608 = 288 ln (1 + r/24)

0.21 = 288 ln ( 1 + r/24)

Divide both sides by 288

0.00072 = ln (1 + r/24)

1.000716527571 = 1 + r/24

r/24 = 0.00072

r = 24 * 0.00072

r = 0.01728

which is same as 1.728%