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On march 9th , Ruth joined a club. Her bank will Automatically deduct 210 kwacha from her account at the end of each month and deposit it into her club account which will earn 5¼% annual interest. The account comes to term on December first . Find: (a) the future value of Ruth's club account (b) Ruth's Total contributions to the account (c) the total interest earned on the account

User Audeoudh
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* Ruth joined the club on March 9th

* Her bank will deduct 210 kwacha from her account at the end of each month

* The deductions will be deposited into her club account

* The club account earns 5.25% annual interest

* The account comes to term on December 1st

* Today is October 16, 2023

To find:

(a) The future value of Ruth's club account on December 1st

(b) Ruth's total contributions to the account

(c) The total interest earned on the account

(a) Future value of the account:

* Ruth made 9 monthly contributions of 210 kwacha from March to November

* So her total contributions were 9 * 210 = 1,890 kwacha

* The interest rate is 5.25% annually, or 0.0525/12 = 0.004375 monthly

* Using the future value of an ordinary annuity formula:

FV = Payment x [(1 + r)^n - 1] / r

= 210 x [(1 + 0.004375)^9 - 1] / 0.004375

= 1,890 x [1.040911125 - 1] / 0.004375

= 1,890 x 0.037810714

= 71.57 kwacha

* So the future value on December 1st is 1,890 + 71.57 = 1,961.57 kwacha

(b) Ruth's total contributions:

* Ruth contributed 210 kwacha for 9 months

* So her total contributions were 210 * 9 = 1,890 kwacha

(c) Total interest earned:

* Future value = 1,961.57 kwacha

* Ruth's contributions = 1,890 kwacha

* So the total interest earned is 1,961.57 - 1,890 = 71.57 kwacha

Therefore:

(a) The future value on December 1st is 1,961.57 kwacha

(b) Ruth's total contributions were 1,890 kwacha

(c) The total interest earned was 71.57 kwacha

User Aresnick
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