Question

Sepand plans to make regular savings contributions of $9,800 per year. His first regular savings contribution is expected later today and his last regular contribution is expected in 11 years. He also plans to make a special savings contribution of $52,000 in 4 years. Sepand expects to earn 9.90 percent per year. How much money does Sepand expect to have in 12 years?

Answer 1

Given,

Annual contributions (A) = $9800

No. of years (n) = 12 years

Special contribution = $52000

Interest rate (r) = 9.90% or 0.099

Solution :-

Future value of annual contributions = A/r x [(1 + r)ⁿ - 1] x (1 + r)

= $9800/0.099 x [(1 + 0.099)¹² - 1] x (1 + 0.099)

= $9800/0.099 x [(1.099)¹² - 1] x (1.099)

= $9800/0.099 x [3.1043616455 - 1] x (1.099)

= $9800/0.099 x 2.1043616455 x 1.099 = $228933.29

Future value of special contribution = special contribution x (1 + r)^{n - 4}

= $52000 x (1 + 0.099)^{12 - 4}

= $52000 x (1.099)⁸

= $52000 x 2.1280485868 = $110658.5265

Total money in 12 years = $228933.29 + $110658.5265 = $339592

Thus, Sepand expect to have $339592 in 12 years.