Question

Suppose that P dollars in principal is invested for t years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period.

=P$10,000, =t112 yr

(a) 1% interest

(b) 4% interest

(c) 4.5% interest

Answer 1

Answer: (a )$30648.54  (b)$882,346.73    (c)  $1,544,700.15

Step-by-step explanation:

Formula: $A=Pe^{rt}$ , where P= principal , r=rate of interest, t= time

Given : P= $10,000, t = 112 years

(a) r = 1% = 0.01

$A=(10000)e^{0.01\times112}$

$A=(10000)e^{1.12}=10000(3.06485420)\approx 30648.54$

Hence, Amount = $30,648.54

(b) r = 4% = 0.04

$A=(10000)e^{0.04\times112}$

$A=(10000)e^{4.48}=10000(88.2346726757)\approx 882346.73$

Hence, Amount = $882,346.73

(c) r = 4.5% = 0.045

$A=(10000)e^{0.045\times112}$

$A=(10000)e^{5.04}=10000(154.470015026)\approx 1544700.15$

Hence, Amount = $1,544,700.15