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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 5.12% 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.)
Expert Solution
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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