22. Peter received a bonus of R100 000 today from his employer. He deposits it into...

22.

Peter received a bonus of R100 000 today from his employer. He deposits it into a savings account that earns 9% interest per annum, compounded annually. He plans to buy a property stand in five years. The property stand he wants to buy currently costs R400 000 and this price is forecast to grow by 6% per annum. Peter plans to use his savings to partially finance his property stand; however, he wants to finance the balance using a bond that will cost 8% interest per annum, compounded annually, over a period of ten years. Calculate the annual payment Peter will have to make on his bond when he buys the property stand.

1. R56 844

2. R153 862

3. R381 42

4. R535 290

Solutions

Expert Solution

Current value of property = 400000, Growth rate of price of property = 6% per annum, No of years to buy the property = 5

Value of property after 5 years = Current value of property (1 + growth rate of price of property) ^{no of years} = 400000 (1 + 6%)⁵ = 400000 x 1.06⁵ = 400000 x 1.3382255776 = 535290.2310

Bonus received = current saving = 100000, rate of interest of savings account = 9% per annum

Value of current savings after 5 years = Current savings (1 + rate of interest of savings account)^{no of years} = 100000 (1 + 9%)⁵ = 100000 x 1.09⁵ = 100000 x 1.5386239549 = 153862.3954

Amount needed to be financed using bond = Value of property after 5 years - Value of current savings after 5 years = 535290.2310 - 153892.3954 = 381427.8356

Rate of interest on bond = 8% per annum, no of years of bond = 10

We can find the annual payment to be made on the bond using pmt function in excel

Formula to be used in excel: = pmt(rate,nper,-pv)

Using pmt function in excel we get annual payment to be made on bond = R56844

Or alternatively we can use the formula to find the annual payment

Let Annual payment = A , Value of financed bond = P , r = rate of interest of bond and n= no of years of bond

A = [P x r x (1 + r)ⁿ] / [(1+r)ⁿ -1] = [381427.8356 x 8% x (1 + 8%)¹⁰] / [(1+8%)¹⁰ -1] = [381427.8356 x 8% x 1.08¹⁰ ] / [1.08¹⁰ - 1] = [381427.8356 x 0.172714] / [2.1589249973 - 1] = 65877.9272 / 1.1589249973 = 56843.9091 = 56844 (rounded to whole number)

Hence Answer is 1. R56844

jeff jeffy answered 11 months ago

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