mary and lewis each open a savings account at the same time. mary invests $3,700 in an account yielding 3.2%…
mary and lewis each open a savings account at the same time. mary invests $3,700 in an account yielding 3.2% simple interest, and lewis invests $3,000 in an account yielding 5.9% simple interest. after fifteen years, who has the greater total amount of money, and how much greater is it?\na. lewis has $879 more than mary.\nb. lewis has $179 more than mary.\nc. mary has $776 more than lewis.\nd. mary has $345 more than lewis.\nplease select the best answer from the choices provided\na\nb\nc\nd
Answer
Explanation:
Step1: Recall simple interest formula
The formula for simple interest is ( I = P \times r \times t ), where ( P ) is the principal amount, ( r ) is the annual interest rate (in decimal), and ( t ) is the time in years. The total amount ( A ) is ( A = P + I ).
Step2: Calculate Mary's total amount
For Mary: ( P = 3700 ), ( r = 0.032 ), ( t = 15 ). First, calculate interest: ( I_{Mary} = 3700 \times 0.032 \times 15 ) ( I_{Mary} = 3700 \times 0.48 = 1776 ) Total amount for Mary: ( A_{Mary} = 3700 + 1776 = 5476 )
Step3: Calculate Lewis's total amount
For Lewis: ( P = 3000 ), ( r = 0.059 ), ( t = 15 ). Calculate interest: ( I_{Lewis} = 3000 \times 0.059 \times 15 ) ( I_{Lewis} = 3000 \times 0.885 = 2655 ) Total amount for Lewis: ( A_{Lewis} = 3000 + 2655 = 5655 )
Step4: Find the difference
Subtract Mary's total from Lewis's total: ( 5655 - 5476 = 179 ) So Lewis has $179 more than Mary.
Answer:
b. Lewis has $179 more than Mary.