40.In the following ordinary annuity, the interest is compounded with each payme

Question

40.In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. How much must you invest each month in a mutual fund yielding 14.7% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.) $

41.Calculate the present value of the annuity. (Round your answer to the nearest cent.) $14,000 annually at 6% for 10 years. $

42.Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Monthly payments on $140,000 at 3% for 25 years. $

43.Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Quarterly payments on $11,500 at 3.5% for 6 years. $

Explanation / Answer

40 Rate on Interest = 14.7% per annum compounded monthly Effective Rate = 14.7%/12 = 1.225% Period = 10 years = 120 months FV = $1000000 This is classic example of future value of annuity FV = P * [(1+r)^n - 1]/r or, 1000000 = P * [(1.01225^ 120 - 1)/0.01225] or, 1000000 = P * 3.310566/0.01225 or, 270.2502P = 1000000 or, P = $3700.274 41 Present Value = P * [1 - (1+r)^-n]/r where P is annuity r is rate of interest n is time period Present Value = 14000 * [1 - 1.06^-10]/0.06 = 14000 * 0.441605 / 0.06 = 14000 * 7.360087 = $103,041.22 42 Present Value = $140,000 Rate = 3% per annum = 0.25% per month Time = 25 years = 300 months Present Value = P * [1 - (1+r)^-n]/r or, 140000 = P * [1 - 1.0025^-300]/0.0025 or, 140000 = P * 0.527191/0.0025 or, P = 140000/210.8765 or, Monthly Payment = $663.90 43 Present Value = $11,500 Rate = 3.5% per annum = 0.875% per quarter Time = 6 years = 24 quarters Present Value = P * [1 - (1+r)^-n]/r or, 11500 = P * [1 - 1.00875^-24]/0.00875 or, 11500 = P * 0.188675/0.00875 or, P = 11500/21.56286 or, Quarterly Payment = $533.32

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