Time Total Amount of the Investment
Total Interest Earned
(years)
(dollars)
(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.
To determine how long Peter and his wife should invest $500 each month with a 5.5% annual interest rate to reach a goal of $25,000, we can look at the interest earned in each year from the table.
In 2 years, they earned $712.28 in interest.
In 3 years, they earned $1,611.14 in interest.
In 4 years, they earned $2,899.15 in interest.
In 5 years, they earned $4,598.26 in interest.
We can see that the interest earned is increasing each year. We need to find the year where the interest earned exceeds $25,000.
From the table, the interest earned in the 5th year is $4,598.26. Since Peter and his wife deposit $500 each month, the total amount they deposit in the 5th year is $500 * 12 = $6,000.
To reach a goal of $25,000, they need to deposit a total of $25,000 - $4,598.26 = $20,401.74.
Since they deposit $6,000 each year, it will take them $20,401.74 / $6,000 = 3.4 years to reach their goal.
Thus, Peter and his wife should invest $500 each month at a 5.5% annual interest rate for 4 years (rounded up from 3.4 years) to reach a goal of $25,000.
If they were to save $500 each month with no interest, it would take them $25,000 / $500 = 50 months to save up $25,000.