Question

Decide which formula to use and than solve

A. Sara borrows $1200 at 8 % simple interest. If the loan is for 5 months, what is the total amount he pays back (This is sometimes called the maturity value)?

B.Sara later decides to deposit $9000 at 7.5% per year compounded annually, and would like to know how much she will have after 10 years.

C. Sara's husband wants to invest $1000 at the end of each quarter at 9% compounded quarterly, and would like to know (1) how much will he have after 10 years? (2) How much interest will he earn after 10 years?

D. Sara is considering depositing $600 at the end of each semi-annual period, for 5 years earning interest of 8%. She would like to know how large a one-time lump sum deposit she could make, at the same rate, to have the same amount of money after 5 years.

Answer 1

A. The amount to be paid back by Sara is $   5000 +5000 * 8/100*5/12 = $ 5166.67 (on rounding off to the nearest cent). The formula is principal + interest and interest = principal * rate of interest * time in years.

B. The amount that Sara would have after 10 years is $ 9000(1+7.5/100)¹⁰ = $ 9000*2.061031562 = $18549.28 (on rounding off to the nearest cent). The formula is Principal (1+rate)^time.

C. The formula for the maturity value of an annuity (F) is F = P[(1+r)ⁿ-1]/r where P is periodic payment, r is the rate of interest per period and n is the no. of periods. Here, P = $ 1000, r = 9/400 and n = 10*4 = 40.Then F = 1000[(1+9/400)⁴⁰]/(9/400) = 1000*400/9 * 2.435188965 = $ 108230.62(on rounding off to the nearest cent). Thus, Sara’s husband would have$ 108230.62 after 10 years.

D. On using the same formula as in C above, F = 600[(1+8/200)]¹⁰/(8/200) = 600*200/8*(1.480244285) = $ 105000. Let Sara make a lump-sum deposit of $ x at the same rate, to have the same amount of money after 5 years. Then x(1+8/200)¹⁰ = 105000 or, 1.480244285 x = 105000 so that x = 105000/1.480244285 = $ 70934.24(on rounding off to the nearest cent). Thus, Sara needs to deposit $ 70934.24 at the same rate, to have the same amount of money after 5 years.