Solve word problem

Question

Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve.

 

Find the accumulated value of an investment of $6000 at 6.5% compounded continuously for 4 years. 

 

Answer 1

To use the first formula, A=P(1+r/n)^nt, you need a (n)umber of compounds per year. Continuous calculation would use the second formula.

 

I did the first formula with daily compounding (365) to show you, and the second formula is with continuous calculation formula. 

 

---------------

(A)

 

A=P(1+r/n)^nt

 

A = $6,000 (1 + 0.065 / 365)^(365 x 4)

 

A = $7,781.40

 

 

(B)

 

A=Pe^rt

 

A = $6,000 x 2.71828^(0.065 x 4)

 

A = $7,781.58

 

 

Answer 2

the underlying formula that you want to use here for continuous compounding is

A = Pe^(rt)

for this set of values that means taking

A = 6000*e^(0.065*4)

A = 6000(1.296934)

A = 7781.604

meaning that the final accumulated value here is $7781.60