Starting on October 1, 2002, annual deposits of $145 are made into an account paying interest at a rate of 7.8% compounded monthly.

Starting on October 1, 2002, annual deposits of $145 are made into an account paying interest at a rate of 7.8% compounded monthly. How much is in the account immediately after the deposit on October 1, 2031? Please show all steps and be very clear thankyou

Expert Solution

Since the payments are annual, we need to first convert the interest rate to effective annual rate.

There are 12 months in a year.

effective annual rate = (1 + interest rate/number of periods)^periods - 1

effective annual rate = (1 + 0.078/12)^12 - 1

effective annual rate = (1 + 0.0065)^12 - 1

effective annual rate = 1.08085 - 1

effective annual rate = 0.08085 or 8.085%

Number of periods = 2031 - 2002 + 1 = 30

Future value = Annuity * [(1 + rate)^periods - 1] / rate

Future value = 145 * [(1 + 0.08085)^30 - 1] / 0.08085

Future value = 145 * [10.30298 - 1] / 0.08085

Future value = 145 * 115.06467

Future value = $16,684.38

The account will have $16,684.38.

jeff jeffy answered 2 years ago

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