1. If you deposit $2,000 into a retirement account earning 6% annually, how much
ID: 2731185 • Letter: 1
Question
1. If you deposit $2,000 into a retirement account earning 6% annually, how much total interest have you earned after 10 years, and how much of that represents interest on the original principal, and how much represents interest earned on accumulated interest? How much additional interest would you earn over the 10 year period if the interest rate were instead 8%?
2. You have just won the lottery. The prize is payable in one of two options. $100,000 now, or $150,000 in eight years. If you have the opportunity to invest at a 5% annual rate of interest, which of the two options would you prefer and why?
3. Your sister would like to borrow $5,000 right now to help her through her last year at college. She says she can easily pay you back $7,000 in ten years after she has finally paid off the rest of her student debt. What annual rate of interest would you earn on this loan if you decide to do it? What else might affect your decision whether to lend to your sister ?
4. You have saved a total of $5,000 in your wedding account. You expect the money in this account to earn 4.5% per year for the foreseeable future. How long would it take for the money to grow to the $8,000 that you think you will need for your dream wedding?
5. What would be the present value today of $10,000 received in 6 years if the interest rate is 6%. Repeat the calculation using a rate of 10%. Give an interpretation of the difference in the two answers.
Explanation / Answer
1. Simple interest is used if only interest in levied on principal. Compound interest is used even interest is accrued subsequent interests also.
Simple interest I = Prt, P is principal, r is annual rate and t is time. So I = 2000*.06*10 = 1200.
To calculate compound interest, I = P(1+r)^n, assuming annual compounding.
So I = 2000*(1.06)^10 = 3581.7.
Hence total interest earned over 10 years is 3581.7, of which 1200 interest is from principal and 2381.7 is from interest.
If interest rate were 10%, using same formula interest realized will be 4317.85, means an additional 736.
2. To answer this, a net present value concept had to be understood.
NPV = c0+ c1/(1+r)..., where c represents cash flow during respective time and r is rate.
In current question,150000 amount after 8 years had to be brought to current date value for comparison.
Hence NPV = 150000/(1+.05)^8 = 101525, which is greater than 100000. Hence taking money after 8 years is a better option.
3. To answer this, again the NPV concept is used.
5000= 7000(/1+r)^10 means r = 3.42%.
Hence for ten years she had been paying at interest rate of 3.42%.
Factors that can influence to give this debt or not will be market interest rates. If market provides better interest rate, of more than 3.42% or not.
4. To answer this, concept of future value is used which works same as present value but opposite way.
FV = PV*(1+r)^n.
8000 = 5000*(1.045)^n
Hence n = 10.68, which is approximately 11 years.
5.
10000 = PV (1+.06)^6
PV = 7049.6
IF RATE USED IS 10%, THEN PV = 5644.73.
Hence, the 1 st case where rate is lesser gives better return in terms of PV.
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