Question

Jan Green established a savings account for her son's college education by making annual deposits of $10,000 at the beginning of each of 5 years to a savings account paying 10%. At the end of the 5th year, the account balance was transferred to a bank paying 10%, and annual deposits of $10,000 were made at the end of each year from the sixth through the eleventh years. What was the account balance at the end of the eleventh year? Future value of 1 for 5 periods of an ordinary annuity at 10%=6.10510.

Answer 1

As Jan Green Make Annual Deposites In the Saving Account At the Beginning of the Year It is the Case of Annuity Due.

Step 1 Calculation of Future Value of Amount in First Bank

F V of Annuity Due = FV of Ordinary (1 + i )

= $ 10000 * 6.10510 * (1 + 0.1)

= $ 67156.1

So at the end of 5th Year Account Balance in First Bank = $ 67156.1

Value of Above amount at the end of eleventh Year = $ 67256.1 (1+0.1)⁶

⁼ $ 67256.1 * 1.771561

= $ 118971.1

Step 2:

Future Value of the Payments made in the Second Bank at the end of 6th to 11th Years

FV of Annuity = Amount Trannsferred * {(1+i)ⁿ - 1} / i

= $ 10000 * {(1+ 0.1)⁶ - 1} / 0.1

= $ 10000 * 7.71561

= $ 77156.1

Step 3:

Calculation of Account Balance at the end of eleventh Year = $ 118971.1 + $ 77156.1

= $ 196127.2