Question

FinancialGoal is $180,000Time 14 years rate is 4.5% compounded monthly. What is periodic deposit at end of each month. What amount of 180000.00 is from deposits and what amount is from interest?

Answer 1

Step-by-step explanation:

Since the goal is to save $180,000 and the periodic payment is made at the end of each period, this is an ordinary annuity problem. The formula for calculating the future value of an ordinary annuity is

S = R[(1 + i)^n -1)/i]

where

R is the periodic payment

i is the interest rate per period

n is the number of periods

S is the future value

From the information given,

S = 180000

r = 4.5% = 4.5/100 = 0.045

Since the period is monthly,

i = r/12 = 0.045/12 = 0.00375

n = 14 x 12 = 168

We want to find R. From the formula,

R = S/[(1 + i)^n -1)/i

By substituting the given values,

R = 180000/[(1 + 0.00375)^168 - 1)/0.00375]

R = 180000/233.45

R = 771.04

Thus, the amount paid monthly = $771.04

If $771.04 is deposited each month,

amount from deposits = 771.04 x 168

amount from deposits = $129534.72

Amount from interest = 180000 - 129534.72

Amount from the interest = $50465.28