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Homework answers / question archive / To purchase a specialty guitar for his band, for the last two years JJ Morrison has made payments of $118 at the end of each month into a savings account earning interest at 5

To purchase a specialty guitar for his band, for the last two years JJ Morrison has made payments of $118 at the end of each month into a savings account earning interest at 5

Finance

To purchase a specialty guitar for his band, for the last two years JJ Morrison has made payments of $118 at the end of each month into a savings account earning interest at 5.12% compounded monthly. If he leaves the accumulated money in the savings account for another year at 5.92% compounded quarterly, how much will he have saved to buy the guitar? The balance in the account will be s| (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

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The balance in the account is computed as shown below:

Future value = Monthly payment x [ [ (1 + r)n – 1 ] / r ]

r is computed as follows:

= 5.12% / 12 (Since the savings are monthly, hence divided by 12)

= 0.426666667%

n is computed as follows:

= 2 x 12 (Since the savings are monthly, hence multiplied by 12)

= 24

So, the amount will be as follows:

= $ 118 x [ [ (1 + 0.00426666667)24 - 1 ] / 0.00426666667 ]

= $ 118 x 25.21528345

= $ 2,975.403447

So, the amount after 1 more year will be as follows:

= Present value x (1 + r)n

= $ 2,975.403447 x (1 + 0.0592 / 4)4 (Interest rate is divided by 4 and time period is multiplied by 4, since the interest rate is

compounded quarterly)

= $ 2,975.403447 x 1.01484

= $ 2,975.403447 x 1.060527255

= $ 3,155.50

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