[latex]FV=P+I[\/latex]<\/p>\r\n\r\n
[latex]t=\\frac{227-43}{365}=\\frac{184}{365} years[\/latex]<\/p>\r\nTherefore,\r\n
[latex]I=Prt=$6,500 \\times 0.085\\times\\frac{184}{365}=$278.52[\/latex]<\/p>\r\nAnd\r\n
[latex]FV=P+I=$6,500+$278.52=$6,778.52[\/latex]<\/p>\r\n\r\n
Key Takeaways<\/p>\r\n\r\n<\/header>\r\n
[latex]FV = P + (Prt)[\/latex]<\/p>\r\n
Factoring out the P, you get<\/p>\r\n
[latex]FV = P(1+rt)[\/latex]<\/p>\r\n\r\n
The future value (or maturity value) is the total amount due at the end of a loan and is calculated by adding the interest due to the original principal.<\/p>\n
[latex]FV=P+I[\/latex]<\/p>\n
2. Calculate the future value (maturity value) of a $6,500 loan at 8.5% (per annum or pa) simple if the loan was taken out on February 12, 2023 and repaid on August 15, 2023.<\/p>\n
First we count the days:<\/p>\n
Using the Calculator:<\/p>\n
DT1 = 2.1223 [ENTER]
\n\u2193DT2 = 8.1523 [ENTER]
\n\u2193[CPT] DBD = 184<\/p>\n
Using Table 3-1:<\/p>\n
[latex]t=\\frac{227-43}{365}=\\frac{184}{365} years[\/latex]<\/p>\n
Therefore,<\/p>\n
[latex]I=Prt=$6,500 \\times 0.085\\times\\frac{184}{365}=$278.52[\/latex]<\/p>\n
And<\/p>\n
[latex]FV=P+I=$6,500+$278.52=$6,778.52[\/latex]<\/p>\n
Key Takeaways<\/p>\n<\/header>\n
<\/p>\n
You can simplify the Future Value equation as follows:<\/p>\n
Since [latex]I = Prt[\/latex] and [latex]FV = P + I[\/latex]<\/p>\n
now, substitute for I. Therefore,<\/p>\n
[latex]FV = P + (Prt)[\/latex]<\/p>\n
Factoring out the P, you get<\/p>\n
[latex]FV = P(1+rt)[\/latex]<\/p>\n