Final answer:
To determine the amount of interest Sandra will receive from her lump sum pension invested at 4.99% compound interest per annum for 8 years, the compound interest formula is applied and the principal amount is subtracted from the accumulated amount after 8 years.
Step-by-step explanation:
Sandra plans to invest a portion of her $26,376 lump sum from her pension for 8 years at a compound interest rate of 4.99% per annum. To calculate the interest Sandra will receive from this investment after 8 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
We will assume that the interest is compounded once per year (n=1). The entire lump sum is invested, so P = $26,376 and the investment time is t=8 years. Therefore:
A = $26,376(1 + 0.0499/1)^(1*8)
After solving for A, we subtract the principal amount P ($26,376) from the accumulated amount A to find the interest earned:
Interest = A - P
After calculating and rounding to the nearest thousand, the answer will give us the amount of interest Sandra will receive after 8 years.