Question

Please show your work and do not use calculators.

You need to accumulate $114,480 for your son's education. You have decided to place equal year-end deposits in a savings account for the next 14 years. The savings account pays 6.88 percent per year, compounded annually. How much will each annual payment be?

Please show your work and do not use calculators.

Answer 1

Given

Future value of amount = $114,480

Number of years = 14years

Rate of interest = 6.88%

Let the amount to be deposited is 'A'

Calculation of annual payment to be made every year (amount in $)

future value = A + [A x (1+i) ] + [A x (1+i)²] + [A x (1+i)³] + [A x (1+i)⁴] + [A x (1+i)⁵] + [A x (1+i)⁶] + [A x (1+i)⁷] + [A x (1+i)⁸] + [A x (1+i)⁹] + [A x (1+i)¹⁰] + [A x (1+i)¹¹] + [A x (1+i)¹²] + [A x (1+i)¹³] $114,480 = A + [A x (1.0688)] + [A x (1.0688)²] + [A x (1.0688)³] + [A x (1.0688)⁴] + [A x (1.0688)⁵] + [A x (1.0688)⁶] + [A x (1.0688)⁷] + [A x (1.0688)⁸] + [A x (1.0688)⁹] + [A x (1.0688)¹⁰] + [A x (1.0688)¹¹] + [A x (1.0688)¹²] + [A x (1.0688)¹³]

Thee right hand side equation is in geometric progression

Here first term is 'A'

Common ratio is '1.0688'

Therefore sum of the progression is A x [1-(1.0688)¹⁴]/[1-1.0688]

$114,480 = A x [1-2.538]/[1-1.0688]

$114,480 = A x [-1.538]/[-0.0688]

$114,480 = A x 22.35

A = $114,480/22.35

A = $5122

Therefore amount to be invested at the end of every year is $5122.