Question

Present Value Computation
Pete Frost made a deposit into his savings account 3 years ago, and earned interest at an annual rate of 8%. The deposit accumulated to $21,000. How much was initially deposited assuming that the interest was compounded (a) annually, (b) semiannually, and (c) quarterly?
Use Excel or a financial calculator for computation. Round your answer to nearest dollar.

(a)	Annually	Answer
(b)	Semiannually	Answer
(c)	Quarterly	Answer

Answer 1

(a)-The amount deposited if the interest was compounded annually

Present Value = Future Value / (1 + r)ⁿ

= $21,000 / (1 + 0.04)³

= $21,000 / (1.08) ³

= $21,000 / 1.259712

= $16,670.48

(b)-The amount deposited if the interest was compounded semi-annually

Present Value = Future Value / (1 + r)ⁿ

= $21,000 / [1 + (0.08/2)]^3x2

= $21,000 / (1.04)⁶

= $21,000 / 1.265319018

= $16,596.61

(c)-The amount deposited if the interest was compounded quarterly

Present Value = Future Value / (1 + r)ⁿ

= $21,000 / [1 + (0.08/4)]^3x4

= $21,000 / (1.02)¹²

= $21,000 / 1.268241795

= $16,558.36