Please help me with this

Question

An account pays interest at a nominal rate of 6% per year. Find the effective annual yield if interest is compounded.

(a) Monthly: effective annual yield= %

(b) Weekly: effective annual yield= %

(c) Daily: effective annual yield= %

Round all answers to three decimal places.

Answer 1

Here's the formula for int:

fv=p(1+int/c)^(n/t)

future value

principal

int

compound=time

years

Answer 2

If the interest were compounded yearly, then effective rate would be the same as nominal rate.

In your example of 6% (= 0.06), initial investment would be multiplied by 1.06 at the end of the year.

In general, if the interest rate is p for any time period, then after that time period the multiplicative factor is (1 + p).

And if the investment remains for n time periods then the multiplicative factor becomes (1 + p)ⁿ.

If the nominal yearly rate is p and a year is divided into n periods

(e.g., 12 months, or 52 weeks), then the rate for each period is p/n,

and hence the multiplicative factor is (1 + p/n) for each period.

If the investment remains for a whole year, i.e., n periods, then the effective yearly rate is (1 + p/n)ⁿ.

In your specific example, p = 0.06.

(a)

n = 12

multiplicative factor = (1 + 0.06/12)¹² = 1.061778

effective annual yield = 6.177%

(b)

n = 52

multiplicative factor = (1 + 0.06/52)⁵² = 1.0617998

effective annual yield = 6.180%

(c)

n = 356

multiplicative factor = (1 + 0.06/356)³⁵⁶ = 1.06183

effective annual yield = 6.183%