Question

Solve the problem. Suppose that P dollars in principal is invested in an account earning 5.3% interest compounded continuously. At the end of 3 yr, the amount in the account has earned $1,378.70 in interest. Find the original principal. Round to the nearest dollar. (Hint: Use the model A = Pert and substitute P + 1,378.70 for A.)

Answer 1

Solve the problem. Suppose that P dollars in principal is invested in an account earning 5.3% interest compounded continuously. At the end of 3 yr, the amount in the account has earned $1,378.70 in interest. Find the original principal. Round to the nearest dollar.

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

`A=P\mleft(e\mright)^{\mleft\{rt\mright\}}`

where

A is the Final Investment Value

I is the interest

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

r=5.3%=0.053

t=3 years

I=$1,378.70

substitute the given values in the formula

Remember that

A=I+P=1,378.70+P

`\begin{gathered} 1,378.70+P=P(e)^{\{0.053\cdot3\}} \\ 1,378.70=P(e)^{\{0.053\cdot3\}}-P \\ 1,378.70=P\lbrack(e)^{\{0.053\cdot3\}}-1\rbrack \\ P=\frac{1,378.70}{\lbrack(e)^{\{0.053\cdot3\}}-1\rbrack} \\ \\ P=\$7,999.98 \end{gathered}`

Round to the whole number

P=$8,000