Asked Feb 19, 2019

Sara decides to set up a retirement fund by depositing $24 at the end of each day for 13 years. How much will she have then, if the interest rate is 6.48% compounded weekly and her account starts with $13487 already deposited?


Expert Answer

Step 1

Let's begin by calculating Effective Interest rate 

Formual for Effective Interest Rate = (1  + (Annual Rate/ number of periods))^ (number of periods)   - 1

                                                                               = (1 + 6.48%/52)^ 52  - 1

                                                                              = 1.066902572   -1   = 0.0669  or 6.69%

Value of $13487 in 13 years will be = $13487 * ( 1 + 6.69%)^13  = $13487 * 2.320715529 = $31299.49

This is what the current sum will grow into. 


Step 2

Now, to calculate the next bit one must know the formula for sum of Geometric Progression  given by:

Sum = First term * (1 - common ratio^n)/ (1 - common ratio)

Now $24 collects everyday for a week and then it is compounded. So, every week $168 (24* 7) gets compounded.

First week's collection will get compounded every week for 13 * 52 = 676 weeks at weekly rate

Seconds week collection will get compounded every week for 675 weeks.

So  let's write the Sum of  Geometric progression for this 

Sum = $168 *  ( 1 + 6.48%/52) ^ 676 + $168 *  ( 1 + 6.48%/52) ^ 675 + $168 *  ( 1 + 6.48%/52) ^ 674 + ........................... + $1...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in



Related Finance Q&A

Find answers to questions asked by student like you

Show more Q&A add

Q: Block, S., Hirt, G., & Danielsen, B. (2017). Foundations of Financial Management. New York, NY: ...

A: Unit sales per month can be compared to production per month and the difference will give us the cha...


Q: The common stock of Company XLT and its derivative securities currently trade in the market at the f...

A: Part (a)Let's denote current stock price as S0, call premium as C, put premium as P, strike price as...


Q: The yield on a default-free four-year zero-coupon bond is 3%; the yield on a default-free five-year ...

A: The spot rate for the year N, given by SN is same as the yield of a zero coupon bond with maturity o...


Q: Please can you show me step by step to solve for OFC? Thank

A: OCF is Operating Cashflow which is the money a firm generates through its regular operations.


Q: 2. Bond valuation The proces value of the cash flows that the security will generate in the future s...

A: A bond’s coupon rate partially determines the interest-based return that a bond will pay and a bondh...


Q: You own 230 shares of stock in Halestorm, Inc., that currently sells for $83.20 per share. The compa...

A: Cum dividend price, P0 = $ 83.20Dividend per share, D = $ 3.30No taxesHence, ex dividend price, Px =...


Q: Francis Inc.'s stock has a required rate of return of 10.25%, and it sells for $25.00 per share. The...

A: Formula to calculate the expected year-end dividend:


Q: A project will produce cash inflows of $3,200 a year for 4 years with a final cash inflow of $5,700 ...

A: Calculation of NPV: Excel spread sheet:


Q: You are creating a portfolio that consists of the following two bonds. Bond A pays an annual 7 perce...

A: We will use the MDURATION function of the excel to calculate the modified duration of bond A.Let's a...