Question

Lee Holmes deposited $17,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $42,000 at 9% interest compounded semiannually. At the end of 6 years, what is the balance in Lee’s account? (Do not round intermediate calculations. Round your answer to the nearest cent.)

Answer 1

Period of deposit of $17,000 is 6 years and that of $42,000 is 3 years (beginning of year 4 to end of year 6). Interest rate is 9% compounded semi annually.

Balance at the end 6 years is the sum of future values of both the deposits.

FV of $17,000 = $28,829.98 calculated as follows:

B C D E 1 Future Value 2 7 3 Future value of an amount is calculated using the formula FV=P(1+r)^n 4 Where P= Principal (Presen Value), 5 n= number of compounding periods 6 r= Rate of interest per period in decimals All amounts in $ 8 Given that 9 Present Value (P)= 17000 No. of years (N)= 10 Rate of interest (% p.a)=R= 9 No. of times compounded a year (t) 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r )=R/(100*t) D10/(100*G10) 0.045 15 No. of periods (n)= N*t G9*G10 12 16 (1+r)= 1+G14 1.045 (1+r)^n= G164615 1.695881433 18 Future value FV= P*(1+r)^n D9*G17 28829.98436 Rounded to $28,829.98 17 19

FV of $42,000 = $54,694.93 calculated as follows:

А B C D 1 Future Value 2 3 Future value of an amount is calculated using the formula FV=P(1+r)^n 4 Where P= Principal (Presen Value), 5 n= number of compounding periods 6 r= Rate of interest per period in decimals All amounts in $ Given that 9 Present Value (P)= 42,000 No. of years (N)= 10 Rate of interest (% p.a)=R= 9 No. of times compounded a year (t): 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r =R/(100*t) D10/(100*G10) 0.045 15 No. of periods (n)= N*t G9*G10 16 (1+r)= 1+G14 1.045 17 (1+r)^n= G164G15 1.302260125 18 Future value FV= P*(1+r)^n D9*617 54694.92524 Rounded to $54,694.93 19 20

Balance at the end 6 years (sum of future values of both the deposits)= $28,829.98 + $54,694.93

= $ 83,524.91