Question

Miller's Hardware plans on saving $100, $150, and $350 at the end of each year for the next three years, respectively. How much will the firm save at the end of the 6th year if it can earn 4% on its savings? (4% is annual interest rate and assume annual compounding) [Please round your answer to the nearest whole number]

Answer 1

We need to use the concept of Future Value for each cash flow to get the solution:

FV = PV * (1+R)^N

where PV = Present Value of Cashflows R = Rate of Interest = 4% = 0.04 N = Number of years/periods

For Cashflow 1 PV₁ = $100 R = 0.04 N = This cashflow will earn interest for 5 years (6^thyear - 1^st year)

FV₁ = $100 * (1+0.04)⁵ = $100 * (1.04)⁵ = $100 * 1.2166529 = $121.665290

For Cashflow 2 PV₂ = $150 R = 0.04 N = This cashflow will earn interest for 4 years (6^thyear - 2^ndyear)

FV₂ = $150 * (1+0.04)⁴ = $150 * (1.04)⁴ = $150 * 1.16985856 = $175.478784

For Cashflow 3 PV₃ = $350 R = 0.04 N = This cashflow will earn interest for 3 years (6^thyear - 3^rdyear)

FV3 = $350 * (1+0.04)³ = $350 * (1.04)³ = $350 * 1.124864 = $393.7024

Amount the firm will save at the end of the 6th year = FV₁ + FV₂ + FV₃  = $121.665290 + $175.478784 + $393.7024

Amount the firm will save at the end of the 6th year = $690.8464 = $690.85

The firm saves an amount of $690.85 at the end of the 6th year.