Question

Please i want a solution for part a. , b , C and D

You have just earned an At on e final examination and graduated with the highest honors. Now that you are working for a living, you have decided to open a savings account. The account is expected to pay a 10% nominal annual interest rate, compounded quarterly, and you wish to save $250,000 at the end of 20 years. Calculate the to be made if they are to be equal and paid at a. the end of each quarter b. the end of each month c. the end of each year d. the beginning of each year

Answer 1

Answer

a)

Explanation: To find the annuity value we use following formula 7'(p) Where. FV- Future Value A - Regular Withdrawal Amount OR Regular Interest OR Regular Dividend OR Installrment Amaunt n Number of Years/Period r Compound Interest Rate rP) Annual Nominal Rate of Interest Given Number of Periods/Years (n) -20 Rate of Interest (r 10% Future Value (FV)- S250000 Calculating Effective Interest Rate Effective Interest can be calculated by following formula, r(2) where r-Effective Rate of Interest rlp-Nominal rate of interest compounded p-times a year iP) 0.1 0.10381 After substituting the values into the formula we have, FV = Al (1 0.10381)20-1 0.1 250000 = A * 2500000.1 (1 + 0.10381)20-1 A $4026.04509 Amount paid quarterly 4026.04509 1006.51127 The amount paid quarterly is $1006.51127.

b)

Explanation: To fird the annuity vallue wuseolkwirg Iormula Vt)-1 PV-A lp) Where. FV Future Value A Regular Withdrawal Amount OR Regular Interest OR Regular Dividend OR Installment Amount n Number of Years Period r Compcund Interest Rate rAinuall Nominal Rate of Interest Given: Number of Periods:Years (n)-20 Rate of Interest (rm)-10% Future Value (FV)-s250000 Calculating Effective Interest Rate Effectiwe Interest carn be celculated by following formula, rle) r-(11 where r-Erfective Rate of Interest Nominal rate of interest p irries a year 0.1 r-(1 11-0.10381 Calculating Nominal Interest Rate Naminal Interest can be calculated by tolloing tormula, where r-Effective Rate of Interest r Nomal rateoierest compourided p ties a year i) 1 12((0.10381)0/11009918 After substituting the values into the forula we have. rlp) (1 0.103811 0.09918 250000 A 2500000.09918 10.10381201 A $3993.03152 Amount paid monthly 3993.03152 332.75263 12 The amount paid monthly is S332.752653.

c)

Explanation To find the annuity value we use following formula FV-A Where FV Future Value OR Amount at time n A - Regular Withdrawal Amount OR Regular Interest OR Regular Dividend OR Installment Amount n - Number of period r Compound interest rate Given Number of periods/years (n) -20 Rate of Interest (ray-1096 Future Value (FV)-$250000 Calculating Effective Interest Rate Effective Interest can be calculated by following formula, lP) where r-Effective Rate of Interest rPl-Nominal rate of interest compounded p-times a year Therefore, elp) 0.1 0.10381 After substituting the values into the formula we have, (+0.10381)0 1 0.10381 250000 A* 2500000.10381 (10.10381)20-1 A $4179.55378 The annuity value is $4179.55378.

d)

Explanation: To find the annuity value we use following formula FV-(1) A Where, FV Future Value OR Amount at time n A Regular Withdrawal Amount OR Regular Interest OR Regular Dividend OR Installment Amount n Number of period r Compound interest rate Given Number of periods/years (n) -20 Rate of interest (ro)-10% Future Value (FV)- $250000 Calculating Effective Interest Rate Effective Interest can be calculated by following formula, where r-Effective Rate of Interest r)-Nominal rate of interest compounded p- times a year Therefore, lp) 0.1 1-(1+ -1-0.10381 After substituting the values into the formula we have, FV (1+r)* Afrac(1+r)n-1r)l (1 0.10381)20 -1 0.10381 250000 (10.10381)A* 2500000.10381 (1 0.10381)(1 0.10381)20-1) A $3786.46944 The annuity value is $3786.46944