On retirement, a manager expects to receive a pension plus a lump sum of RM60000. He wants to obtain an annual income of RM7000 by investing the lump sum in loan stock yielding 13% and a deposit account yielding 9%. What amount should be invested in each case? (Assuming nothing held in cash)

To determine how much should be invested in loan stock yielding 13% and how much in the deposit account yielding 9% to obtain an annual income of RM7000, we can set up a system of two equations based on the interest earned from each investment. Let's use the following variables: Let x represent the amount invested in loan stock at 13%. Let y represent the amount invested in the deposit account at 9%. We know the following information: The total amount invested should be the lump sum of RM60000, so: x + y = 60000 The annual income from the loan stock (13%) and deposit account (9%) should sum up to RM7000: 0.13x + 0.09y = 7000 Now, you have a system of two equations: x + y = 60000 0.13x + 0.09y = 7000 You can solve this system of equations using either substitution or elimination. Here, I'll use the elimination method. First, let's multiply the second equation by 100 to get rid of decimals: x + y = 60000 13x + 9y = 700000 Now, you can multiply the first equation by 9 to match the coefficients of y: 9x + 9y = 540000 Now, subtract the first equation from the second equation to eliminate y: (13x + 9y) - (9x + 9y) = 700000 - 540000 4x = 160000 Now, divide both sides by 4 to solve for x: 4x / 4 = 160000 / 4 x = 40000 So, the manager should invest RM40,000 in loan stock yielding 13%. Now, you can find the amount to invest in the deposit account by using the first equation: x + y = 60000 40000 + y = 60000 Subtract 40000 from both sides to solve for y: y = 60000 - 40000 y = 20000 The manager should invest RM20,000 in the deposit account yielding 9%.