Problema Solution
pam wants to invest the same amount at the end of every 3 months so that he will have 4000 in 3 years. The account will pay 6% compounded quarterly. How much should he deposit each quarter.
Answer provided by our tutors
A sequence of equal payments made at equal periods of time is called an annuity. If the payments are made at the end of the time period, and if the frequency of payments is the same as the frequency of compounding, the annuity is called an ordinary annuity.
S = R[((1 + i)^n-1)/i]
S = $4,000 is the future value of an Ordinary Annuity ;
R = is the periodic payment;
i = 0.06/4 is the interest rate per period (every quarter)
n = 4*3 = 12 period is the number of periods
R[((1 + 0.06/4)^12 -1)/(0.06/4)] = 4000
R[(1.015^12 - 1)/0.015] = 4000
by solving we find:
R = $306.72
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Pam should deposit $306.72 each quarter (every 3 months).