Question

Miller's Hardware plans on saving $100, $150, and $400 at the end of each year for the next three years, respectively. How much will the firm save at the end of the 7th year if it can earn 2% on its savings? (2% is annual interest rate and assume annual compounding) [Please round your answer to the nearest whole number]

Answer 1

Compounded amount formula = principle amount(opening amount) x (1+r)^n

R = rate of interest i. E =2 % per annum

N = period of compounding

Save at the end of 1st year = $100

Save at the end of 2nd year =

Principle amounts = $100

Rate = 2%

N = 1 year

Deposit at the end = $150

=$100 x (1.02)^1 + $150

= $102 + $150 = $252

Save at the end of 3rd year = $252 x (1.02)^1 + $400

= $257.04 + $400 = $657.04

Save at the end of 7th year =

N = 7 year - 3 year = 4 years

Rate = 2%

Principle amount = $657.04

= $657.04 x (1.02)^4

= $657.04 x 1.08243

=$711.20

Alternatively

For $100,

N = 6 years

Rate = 2 %

For $150

N = 5 years

Rate = 2%

For $400

N = 4 years

Rate = 2%

So,

=(100 x (1.02)^6) +(150 x (1.02)^5) + (400 x (1.02)^4)

=$112.62 + $165.61 + $432.97

= $711.20

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