# Chapter 8 - Personal Finance - 8.3 Simple Interest - Exercise Set 8.3: 45

(a) $A = 275~t+ 5000$ (b) The slope of the function is 275. The rate of change of the value in the account is $\$275$per year. #### Work Step by Step (a) This is the formula we use when we make calculations with simple interest:$A = P~(1+rt)A$is the future value$P$is the principal$r$is the interest rate$t$is the number of years We can express the future value in the account as a linear function of time,$t$.$A = P~(1+rt)A = (5000)~[1+(0.055)t]A = 275~t+5000$(b) The future value in the account is$A = 275~t+5000$The slope of the function is 275. This means that the account increases in value by$\$275$ per year. That is, the rate of change of the value in the account is $\$275\$ per year.

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