Final answer:
The value of a $100 deposit after five years, with the interest rate starting at 5% and increasing by one percentage point each year, is $135. This is calculated by finding the simple interest for each year individually and then adding them up.
Step-by-step explanation:
To calculate the value of a $100 deposit at 5% interest for the first year, with the interest rate increasing by one percentage point each subsequent year, you can use the simple interest formula which is principal × interest rate × time. Since the interest rate increases each year, the calculation for each year must be done separately and then all the interests accumulated over five years should be added to the initial principal.
Simple Interest Calculation
For the first year: $100 × 0.05 × 1 = $5
Second year (6%): $100 × 0.06 × 1 = $6
Third year (7%): $100 × 0.07 × 1 = $7
Fourth year (8%): $100 × 0.08 × 1 = $8
Fifth year (9%): $100 × 0.09 × 1 = $9
The total interest earned over five years is $5 + $6 + $7 + $8 + $9 = $35. Therefore, the total value after five years is $100 + $35 = $135.