If Mrs. Smith lives to age 88 (she is now retiring at 65 years) what annual APR will result in the 420000 reaching a balance of 1000000 upon her death, if she deposits them in an account that offers monthly compounding?
P = Po(1+r)^n = $1,000,000
Po = $420,000
r=Monthly % rate expressed as a decimal.
n = 12comp/yr * 23yrs = 276 Compounding
periods.
P = 420,000(1+r)^276 = 1,000,000
(1+r)^276 = 1,000,000/420,000 = 2.38095
276*Log(1+r) = Log 2.38095
Log(1+r) = Log 2.38095/276 = 0.00136504
1+r = 10^(0.00136504) = 1.00314807
r = 0.00314807/mo.
APR = 0.00314807/mo * 12mo/yr = 0.0378 =
3.78%.