rafael plans to set aside money for his young daughters college tuition. he will deposit money in an…

rafael plans to set aside money for his young daughters college tuition. he will deposit money in an ordinary annuity that earns 6.6% interest, compounded monthly. deposits will be made at the end of each month. how much money does he need to deposit into the annuity each month for the annuity to have a total value of $72,000 after 15 years? do not round intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

rafael plans to set aside money for his young daughters college tuition. he will deposit money in an ordinary annuity that earns 6.6% interest, compounded monthly. deposits will be made at the end of each month. how much money does he need to deposit into the annuity each month for the annuity to have a total value of $72,000 after 15 years? do not round intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Identify the formula

The formula for the future value of an ordinary annuity is ( FV = A\times\frac{(1 + r)^{n}-1}{r} ), where ( FV) is the future value, ( A) is the annuity payment (monthly deposit), ( r) is the interest rate per period, and ( n) is the number of periods. First, find ( r) and ( n). The annual interest rate ( i=6.6%=0.066). Since the interest is compounded monthly, ( r=\frac{0.066}{12}=0.0055). The time ( t = 15) years, and the number of months ( n=15\times12 = 180). The future value ( FV=$72000).

Step2: Solve for ( A)

From ( FV = A\times\frac{(1 + r)^{n}-1}{r}), we can rewrite it as ( A=\frac{FV\times r}{(1 + r)^{n}-1}). Substitute ( FV = 72000), ( r=0.0055), and ( n = 180) into the formula: ((1 + r)^{n}=(1+0.0055)^{180}). Using the formula ( a^{b}) (where ( a = 1.0055) and ( b=180)), ((1.0055)^{180}\approx2.757). Then ( (1 + r)^{n}-1=2.757-1 = 1.757). ( A=\frac{72000\times0.0055}{1.757}). (72000\times0.0055 = 396). (A=\frac{396}{1.757}\approx225.4).

Answer:

(225.40)