Thread: Gic fv

A bank offers a rate of 5.3% compounded semiannually on its four -year GICs. What monthly and annually compounded rates should it quote in order to have the same effective interest rate at all three nominal rates?

{___|____|____|_____|_____}
0 yr1 yr2 yr3 yr4

P =
i = 5.3%/2
n = 4

p(1 + 0.053/2)^2 * 4

That's as far as i got and after that i am stuck on what to do next?

Originally Posted by diehardmath4

A bank offers a rate of 5.3% compounded semiannually on its four -year GICs.

The fact that this rate is on 4year GIC's has nothing to do with solution.
The question can be simplified to:
what annually compounded rate and what monthly compounded rate
is equivalent to 5.3% compounded semiannually?

5.3 cpd s/a = (1 + .053/2)^2 - 1 = 1.05370225 - 1 = .0537 :
that's 5.37% annually (approximately).

For monthly, you need a rate that achieves 5.37 when compounded 12 times:
(1 + r/12)^12 = 1.0537
1 + r/12 = 1.0537^(1/12)
r/12 = 1.0043685 - 1
r/12 = .0043685
r = .052422 : 5.24% (approximately)

SO: both 5.37 cpd annually and 5.24 cpd monthly = 5.3 cpd semiannually.

Ya'll ok with that?