Question

Hannibal opens a savings account on January 1, 1984 with a deposit of 330 dollars, and continues to make deposits of the same amount at the beginning of each month until January 1, 1990, when he makes the final deposit. If the account pays a nominal rate of interest of 4.7 percent convertible monthly, how much is in the account on January 1, 1998?

(1 point) Hannibal opens a savings account on January 1, 1984 with a deposit of 330 dollars, and continues to make deposits of the same amount at the beginning of each month until January 1, 1990, when he makes the final deposit. If the account pays a nominal rate of interest of 4.7 percent convertible monthly, how much is in the account on January 1, 1998? Answer = dollars.

Answer 1

In order to find the amount in saving account on January 1,1990, we need to calculate future value of annuity compounded monthly at the rate of 4.7%, it can be calculated as follows:

FV = P * { (1+i)ⁿ - 1 / i } * (1 + i)

Here,

i = Interest rate in decimals

n = number of compounding periods

Since, there are 12 months and the tenure of deposit is 6 years, so compounding time will be 12 * 6 = 72, because the payment is made at the beginning of every month, the formula will be multiplied with (1+i)

FV = $330 * { 1 + 0.0040)⁷² - 1 / 0.0040 } * (1 + 0.0040}

     = $330 { 1.333 - 1 / 0.0040} * 1.0040

     = $330 * 83.25 * 1.0040

     = $330 * 83.583

    = 27,582.40