Question

You deposit $12,000 in an account that pays 6.5% interest compounded quarterly. Use the future value formula for simple interest to determine the effective annual yield.

Answer 1

6.67%

Explanation:

The formula for accrued value A on a deposit P for t years compounded n times annually at i% APR is

`A = P\left(1 + (r)/(n)\right)^(nt)`

where r = i/100 i.e the interest rate as a decimal

We are given
P = $12,000

i = 6.5%

r = 6.5/100 = 0.065

n = 4 since interest is compounded annually

t = 1 year since we are interested in the annual yield

`\begin{aligned}A &= 12000\left(1 + (0.065)/(4)\right)^(4\cdot 1)\\& = 12000(1 + 0.01625)^4\\&= 12000(1.01625)^4\\& = \$12,799.22\end{aligned}`

Effective Annual Interest = 12,799.22 - 12,000 = $799.22
This works out to an annual yield of 799.25/12000

= 0.0667

= 6.67%