Question

Claire made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Claire doesn’t touch the money in her account, she can find the amount she’ll have the next year by multiplying her current amount by 1.03. A) how much money will Claire have in her account after 1 year? After 2 years? B) how much money will Claire have in her account after 5 years? Explain your reasoning. C) Write an expression for the amount of money Claire would have after 30 years if she never withdraws money from that account.

Answer 1

We can make and use the equation: A = 160( 1.03 )^y: A = amount, 160 = amount put in, 1 + .03 = 1.03 = interest, and y as the number of years, as the money is compounded every year. (This is the compound interest equation, but I put in the numbers)

A) 160 * 1.03 = $164.80, 160 * 1.03² = $169.744 ≈ $169.74

B) 160 * 1.03⁵ = 185.48385 ≈ $185.48

The expression is the same as saying (((((160 * 1.03)1.03)1.03)1.03)1.03). This is like multiplying 160 * 1.03, which gives the amount for the first year. Then, that amount is multiplied by 1.03, which is the amount for the second year. This isi repeated until 5 years.

C) 160(1.03)³⁰