Use the table to answer the question.
Time
(years)
Total Amount of the Investment
(dollars)
Total Interest Earned
(dollars)
2 12,712.28 712.28
3 19,611.14 1,611.14
4 26,899.15 2,899.15
5 34,598.26 4,598.26
Peter and his wife want to buy a house, and they are planning to save $500 each month for the down payment.
The table shows how much interest Peter and his wife can earn if they invest $500 each month with a 5.5% annual interest rate, compounded monthly.
If the goal is to save at least $25,000 for the down payment, how long should Peter and his wife invest $500 each month? How long would it take to save $25,000 if they were to save $500 each month with no interest?
(1 point)
Peter and his wife should invest $500 monthly at 5.5% annual interest for
years. With no interest, it would take them
months to save up $25,000.
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To find out how long Peter and his wife should invest $500 each month at a 5.5% annual interest rate to save at least $25,000, we can use the table. We can see that after 5 years of investing, they would have a total amount of $34,598.26. Since this amount exceeds $25,000, they would need to invest for less than 5 years.
To estimate how long it would take for them to reach $25,000, we can look at the total interest earned in each year. In the first year, they earn $712.28 in interest. Each subsequent year, the interest earned increases by approximately $900. So, to reach $25,000, we can estimate that it would take about 2 years and 9 months (or 2.75 years) of investing.
If they were to save $500 each month with no interest, it would take them $25,000/$500 = 50 months to reach the goal.