Answer:
Principal = $23,392.45
Explanation:
To solve this, we are required to find a certain amount invested for 35 years at an interest rate of 4.1% compounded annually, yielding $98,000.
The formula for compounded interest is used, and this is done as follows:
[tex]FV=PV(1+\frac{r}{n} )^{nt}\\Where:\\FV=Future\ value\ =\ \$98,000\\PV= Present\ value\ =\ ???\\r= interest\ rate\ = 4.1\%=0.041\\n = number\ of\ compounding\ periods\ per\ year\ = monthly\ = \ 12\\ t= time\ =\ 35\ years[/tex]
[tex]98000=PV(1+\frac{0.041}{12} )^{(12\times35)}\\98000=PV(1+0.003417)^{420}\\98000=PV(1.003416667)^{(420)}\\98000=PV(4.189386)\\PV= \frac{98000}{4.189386} \\\\=PV= \$23,392.45[/tex]
Therefore, the principal is approximately $23,392
