Question

Conctext:Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compoundsmonthly. How much will the CD be worth in 10 years?Question:Lori gets an offer from another bank that is also paying 6% on CD’s, but is compounding interest daily. How much will the CD be worth in 10 years?

Answer 1

Compound Interest

The final value of an investment of P dollars for t years at an interest rate of r is given by:

`FV=P\mleft(1+(r)/(m)\mright)^(m\cdot t)`

Where m is the number of compounding periods per year.

(a)

Lori buys a CD for P = $1500 that earns r = 6% = 0.06 interest compounded monthly for t = 10 years. Here m = 12 because there are 12 months in a year.

Substituting:

`\begin{gathered} FV=1500\mleft(1+(0.06)/(12)\mright)^(12\cdot10) \\ \text{Calculate:} \\ FV=1500(1.005)^(120) \\ FV=2729.10 \end{gathered}`

The CD will be worth $2729.10 in 10 years.

(b) If the interest compounds daily, then m = 360. Calculating:

`\begin{gathered} FV=1500\mleft(1+(0.06)/(360)\mright)^(360\cdot10) \\ FV=1500(1.0001666)^(3600) \\ FV=2733.04 \end{gathered}`

The CD will be worth $2733.04 in 10 years.

(c) For t = 5 years:

`\begin{gathered} FV=1500\mleft(1+(0.06)/(360)\mright)^(360\cdot5) \\ FV=1500(1.0001666666)^(1800) \\ FV=2024.74 \end{gathered}`

The CD will be worth $2024.74 in 5 years.