Question

Find QUARTERLY payment. Please show the formula as well:

FV = 300,000

Rate = 8.4% compounded MONTHLY

PV = 0

Period = 20 years

Answer 1

first we have to find quarterly rate for monthly compounding

Effective annual rate formula = (1 + (r/n))^n - 1

where r = annual rate

n = number of compoundings

so,

[(1+ (8.4/12))^12] - 1 = [(1+x)^4] - 1 (x = quarterly rate)

quarterly rate = 2.115%

future value of annuity = P*[(1+r)^n - 1 / r ]

P = Quarterly payments

here n = 20*4 = 80

300,000 = P*[(1+2.115%)^80 - 1 / 2.115% ]

P = 300,000 / 204.95457

Quarterly Payments = $1463.739 (rounded to three decimals)

(it is assumed that above quarterly payments occur at the end of each quarter.other wise(if at beginning) answer would be different.)