# E.A.R.

If an investment of \$4,000 will grow to \$6,520 in four years with monthly compounding, the effective annual interest rate will be closest to: A. 11.21%. B. 12.28%. C. 12.99%. D. 15.75%. Answer : C. 12.99% I keep getting 12.28 %. 4000*(1+monthly rate)^48 = 6520 monthly rate = 1.023% EAR = 1.023 *12 = 12.28 % What am I missing here?

You’re close 1.023 is the monthly rate, so then use (1 + 0.01023)^12 -1 to get the EAR

Duh!

yeah well, I would feel better about it if I hadn’t had to have gone back to my notes to solve it! uh oh…

Just do it this way: PV=(\$4,000) N=4; FV=\$6,520; N=4; I=??= it works out the same way.

busprof Wrote: ------------------------------------------------------- > Just do it this way: PV=(\$4,000) N=4; FV=\$6,520; > N=4; I=??= > > it works out the same way. you have to switch the compounding periods to 12 though on the calculator

you could use N=48 and avoid the trouble of going to 12 compounding periods and then having to remember to switch back. if you did N=48 and CPT I/Y - u would get the monthly I/Y automatically. (and then you do not have to remember to switch back to a yearly compounding period, which if you did forget would ensure you could your next TVM problem wrong (maybe on bonds, maybe somewhere else, like on leases during the FSA section).

tlb Wrote: ------------------------------------------------------- > busprof Wrote: > -------------------------------------------------- > ----- > > Just do it this way: PV=(\$4,000) N=4; > FV=\$6,520; > > N=4; I=??= > > > > it works out the same way. > > you have to switch the compounding periods to 12 > though on the calculator Actually, you don’t. Check and see. Using N=48 and then compounding to an EAT will give you the same interest rate as using N=4.

4000*(1+EAR)^4 =6520 EAR = (1.63^0.25)-1 = 0.1299 =12.99% You can actually ignore the whole thing about 48 monthly payments…

EAR=[(FV/PV)^(1/n)]-1=[(6520/4000)^0.25]-1=12.99%