Question

O CONSUMER MATHEMATICS Finding the future value of an annuity The Wilson family wants to save money to travel the world. They purchase an annuity with a monthly payment of $53 that earns 4% interest, compounded monthly Payments will be made at the end of each month. Find the total value of the annuity in 14 years Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. X 5 ?

Answer 1

Solution :-

To find future value we will use following formula: FV = Future Value C = Regular deposit amount |(1+i)" – 1 FV = C: i = Interest rate per period n = number of periods In this example the number of periods is n= 14 years · 12 = 168, the interest rate per period is i = 0,04 = 0.003333, and the regular deposit is C = 53. After substituting the values into the formula we have: 12 |(1+i)" – 1 FV = C:1 [(1+0.003333)168 – 1] FV = 53. 0.003333 1.003333168 – 1] FV = 53 0.003333 FV = 53 224.705971 FV = 11909.42

The future value of 168 monthly deposits of $53.00, deposited at the end of each period, and earning an annual interest rate of 4.000%, would be $11,909.78 -- of which $8,904.00 is the total of the payments and $3,005.78 is the total interest earnings. Please note that the $3,005.78 also represents the financial opportunity cost of spending $53.00 per month for 14 years on non-essential expenditures that lose their value with time and/or use.

Year Interest Payments $636 $636 $12 $38 Balance $648 $1,322 $2,024 $2,754 $636 $66 $636 $94 $636 $124 $3,514 $636 $636 $155 $187 $4,305 $5,128 $636 $221 $5,985 $636 $256 $6,876 $636 $7,804 $292 $330 $636 $8,770 $636 $369 $9,775 $636 $410 - 14 $636 $453 $3,006 $10,821 $11,910 $11,910 Totals $8,904